@article{Kolm41,
author = {A.N. ~Kolmogorov},
title = "{The local structure of turbulence in incompressible viscous fluid for
very large Reynolds numbers}",
journal = {C. R. Acad. Sci. URSS},
volume = {30(4)},
pages ={301--305}, 
year =1941
}

@article{Mig83,
author = {A.~Migdal}, 
title = "{ Loop equations and $\inv{N}$ expansion}",
journal = {Physics Reports}, 
volume = 201, 
page =102,
year = 1983
}

@misc{Umeki,
author ="{ Makoto Umeki}", 
publisher={Tokyo University Preprint},
year = 1993,
month = "July",
url = {https://arxiv.org/abs/hep-th/9307144}
}

@misc{KH20,
   author = "Wikipedia",
   title = "{Kelvin-Helmholtz instability} --- {W}ikipedia{,} The Free Encyclopedia",
   year = "2020",
   url = {https://en.wikipedia.org/wiki/Kelvin-Helmholtz_Instability
   },
   note = "[Online; accessed 29-October-2020]"
}
@misc{RHP,
   author = "Encyclopedia of Mathematics",
   title = "{Boundary value problem, complex-variable methods. Encyclopedia of Mathematics.}",
   year = "2020",
   url = {http://encyclopediaofmath.org/index.php?title=Boundary_value_problem,_complex-variable_methods&oldid=46131},
   note = "[Online; accessed 30-May-2020]"
}
@misc{GLQ,
   author = "Wikipedia",
   title = "{Gauss-Legendre quadrature} --- {W}ikipedia{,} The Free Encyclopedia",
   year = "2020",
   url = {https://en.wikipedia.org/wiki/Gauss%E2%80%93Legendre_quadrature},
   note = "[Online; accessed 9-November-2020]"
}
@misc{DL21,
   author = "Wikipedia",
   title = "{Double layer (surface science)} --- {W}ikipedia{,} The Free Encyclopedia",
   year = "2021",
   url = {https://en.wikipedia.org/wiki/Double_layer_(surface_science)},
   note = "[Online; accessed 24-January-2021]"
}
@article{Cvitanovi__2010,
	doi = {10.1088/0031-8949/2010/t142/014007},
	url = {https://doi.org/10.1088/0031-8949/2010/t142/014007},
	year = 2010,
	month = {dec},
	publisher = {{IOP} Publishing},
	volume = {T142},
	pages = {014007},
	author = {P Cvitanovi{\'{c}} and J F Gibson},
	title = {Geometry of the turbulence in wall-bounded shear flows: periodic orbits},
	journal = {Physica Scripta},
	abstract = {The dynamical theory of moderate Reynolds number turbulence triangulates the infinite-dimensional Navier–Stokes state space by sets of exact solutions (equilibria, relative equilibria, periodic orbits, etc), which form a rigid backbone that enables us to describe and predict the sinuous motions of a turbulent fluid. We report on the determination of a set of unstable periodic orbits from close recurrences of the turbulent flow. A few equilibria that closely resemble frequently observed but unstable coherent structures are used for constructing a low-dimensional state-space projection from the extremely high-dimensional data sets. The turbulent flow can then be visualized as a sequence of close passages to unstable periodic orbits, i.e the time-recurrent dynamical coherent structures typical of a turbulent flow.
	}
	}
	
@misc{SIF,
   author = "Wikipedia",
   title = "{Schwarz integral formula} --- {W}ikipedia{,} The Free Encyclopedia",
   year = "2021",
   url = {https://en.wikipedia.org/wiki/Schwarz_integral_formula#:~:text=In%20complex%20analysis%2C%20a%20branch,values%20of%20its%20real%20part.},
   note = "[Online; accessed 16-October-2020]"
}
@article{MBO82, 
title={Analytic structure of vortex sheet dynamics. Part 1. Kelvin–Helmholtz instability}, 
volume={114}, 
DOI={10.1017/S0022112082000159}, 
journal={Journal of Fluid Mechanics}, 
publisher={Cambridge University Press}, author={Meiron, Daniel I. and Baker, Gregory R. and Orszag, Steven A.},
year={1982}, 
pages={283–298}
}


@article{QG, 
author = "{D.~Gross , A.~Migdal}",  
title = {A NONPERTURBATIVE TREATMENT OF TWO-DIMENSIONAL
QUANTUM GRAVITY},
journal = {Nuclear Physics}, 
volume = {B335}, 
page =635,
year = 1990
}

@article{EF11,
author = {Eames, I.  and Flor, J. B. },
journal = {Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences},
volume = {369},
number = {1937},
pages = {702-705},
year = {2011},
title = {New developments in understanding interfacial processes in turbulent flows},
doi = {10.1098/rsta.2010.0332},
url = {https://royalsocietypublishing.org/doi/abs/10.1098/rsta.2010.0332},
eprint = {https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.2010.0332}
}
@incollection{Feynman,
  author={Feynman, Richard P and Leighton, Robert B and Sands, Matthew},
  editor={Gottlieb, Michael A. and Pfeiffer, Rudolf},
  booktitle={The Feynman lectures on physics, Vol. I: Mainly mechanics, radiation, and heat},
  title={3-7 How did it get that way?},
  volume={1},
  year={2011},
  publisher={Basic books},
  url={https://www.feynmanlectures.caltech.edu/I_03.html},
}
@Article{Rosenhead1931,
author={Rosenhead, L.},
title={The Formation of Vortices from a Surface of Discontinuity},
journal={Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character},
year={1931},
month={2020/10/24/},
publisher={The Royal Society},
volume={134},
number={823},
pages={170-192},
note={Full publication date: Nov. 3, 1931},
issn={09501207},
url={http://www.jstor.org/stable/95835}
}



@incollection{BURGERS1948,
title = "A Mathematical Model Illustrating the Theory of Turbulence",
editor = "Richard {Von Mises} and Theodore {Von Kármán}",
booktitle = "Advances in Applied Mechanics",
publisher = "Elsevier",
volume = "1",
pages = "171 - 199",
year = "1948",
issn = "0065-2156",
doi = "https://doi.org/10.1016/S0065-2156(08)70100-5",
url = "http://www.sciencedirect.com/science/article/pii/S0065215608701005",
author = "J.M. Burgers"
}
% A.A. Townsend. On the fine-scale structure of turbulence. Proc. Roy. Soc. Lond.
% Ser. A., 208(1095):534–542, 1951. doi: 10.1098/rspa.1951.0179.
@ARTICLE{TW51,
author = {{Townsend}, A.~A.},
        title = "On the fine-scale structure of turbulence",
      journal = {Proc. Roy. Soc. Lond. Ser. A.},
         year = 1951,
       volume = {208(1095)},
        pages = {534–542},
        doi = {10.1098/rspa.1951.0179.},
}
@ARTICLE{BM05,
       author = {{Bazant}, M.~Z. and {Moffatt}, H.~K.},
        title = "{Exact solutions of the Navier Stokes equations having steady vortex structures}",
      journal = {Journal of Fluid Mechanics},
         year = 2005,
        month = oct,
       volume = {541},
        pages = {55-64},
          doi = {10.1017/S0022112005006130},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2005JFM...541...55B},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@article{MKO94, 
title={Stretched vortices – the sinews of turbulence; large-Reynolds-number asymptotics}, 
volume={259}, 
DOI={10.1017/S002211209400011X}, 
journal={Journal of Fluid Mechanics}, publisher={Cambridge University Press}, 
author={Moffatt, H. K. and Kida, S. and Ohkitani, K.}, 
year={1994}, 
pages={241–264}
}
@article{Brady98,
  title={Regularized Vortex Sheet Evolution in Three Dimensions},
  author={M. Brady and A. Leonard and D. Pullin},
  journal={Journal of Computational Physics},
  year={1998},
  volume={146},
  pages={520-545}
}
@inproceedings{M88,
    author={A. A. Migdal},
    title={Random Surfaces and Turbulence},
    year={1988},
    booktitle={Proceedings of the International Workshop on Plasma Theory and Nonlinear and Turbulent Processes in Physics, Kiev, April 1987},
    editor ={V. G. Bar’yakhtar},
    pages ={460},
    bookyear={1988},
    publisher={World Scientific}
}

@article{AM89,
title = "Dynamics of vortex surfaces in three dimensions: Theory and simulations",
journal = "Physica D: Nonlinear Phenomena",
volume = "40",
number = "1",
pages = "91 - 118",
year = "1989",
issn = "0167-2789",
doi = "https://doi.org/10.1016/0167-2789(89)90029-8",
url = "http://www.sciencedirect.com/science/article/pii/0167278989900298",
author = "Michael E. Agishtein and Alexander A. Migdal"
}

@ARTICLE{Kaneda90,
       author = {{Kaneda}, Yukio},
        title = "{On the three-dimensional motion of an infinitely thin vortex sheet in an ideal fluid}",
      journal = {Physics of Fluids A},
     keywords = {Computational Fluid Dynamics, Euler-Lagrange Equation, Ideal Fluids, Three Dimensional Motion, Vortex Sheets, Flow Velocity, Symmetry, Three Dimensional Flow, Two Dimensional Flow, Fluid Mechanics and Heat Transfer},
         year = 1990,
        month = oct,
       volume = {2},
       number = {10},
        pages = {1817-1826},
          doi = {10.1063/1.857708},
       adsurl = {https://ui.adsabs.harvard.edu/abs/1990PhFlA...2.1817K},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@article{Kuz18,
author = {Agafontsev, Dmitry and Kuznetsov, E.A. and Mailybaev, Alexei},
year = {2018},
month = {09},
pages = {095104},
title = {Development of high vorticity structures and geometrical properties of the vortex line representation},
volume = {30},
journal = {Physics of Fluids},
doi = {10.1063/1.5049119}
}
@incollection{M93,
    pages = {193--231},
    author = {Alexander Migdal},
    title = {Loop Equation and Area Law in Turbulence},
    url = {https://arxiv.org/abs/hep-th/9310088},
    doi = {10.1007/978-1-4615-1819-8},
    year = {1995},
    publisher = {Springer {US}},
    editor = {Laurent Baulieu and Vladimir Dotsenko and Vladimir Kazakov and Paul Windey},
    booktitle = {Quantum Field Theory and String Theory},
}

@article{Hal20,
    author = {Halawa, B. and Merhi, S. and Tang, C. and Zhou, Q.},
    year = {2020},
    month = {03},
    pages = {},
    title = {Three-dimensional visualization of stratified turbulent wakes at varying Reynolds number},
    volume = {23},
    journal = {Journal of Visualization},
    doi = {10.1007/s12650-020-00638-x}
}
@inproceedings{FP85,
  title={On the singularity structure of fully developed turbulence Turbulence and Predictability},
  booktitle={Geophysical Fluid Dynamics: Proc. Intl School of Physics E. Fermi },
  author={Parisi, G and Frisch, U},
  year={1985},
  pages = {84-88},
  editor= {M Ghil, R Benzi and G Parisi},
  publisher={Amsterdam: North-Holland}
}

@article{BK07,
   title={Burgers turbulence},
   volume={447},
   ISSN={0370-1573},
   url={http://dx.doi.org/10.1016/j.physrep.2007.04.002},
   DOI={10.1016/j.physrep.2007.04.002},
   number={1-2},
   journal={Physics Reports},
   publisher={Elsevier BV},
   author={BEC, J and KHANIN, K},
   year={2007},
   month={Aug},
   pages={1–66}
}

@article{Polyakov_1995,
	doi = {10.1103/physreve.52.6183},
  
	url = {https://doi.org/10.1103%2Fphysreve.52.6183},
  
	year = 1995,
	month = {dec},
  
	publisher = {American Physical Society ({APS})},
  
	volume = {52},
  
	number = {6},
  
	pages = {6183--6188},
  
	author = {A. M. Polyakov},
  
	title = {Turbulence without pressure},
  
	journal = {Physical Review E}
}
@Article{SY05,
author={Yakhot, Victor
and Sreenivasan, Katepalli R.},
title={Anomalous Scaling of Structure Functions and Dynamic Constraints on Turbulence Simulations},
journal={Journal of Statistical Physics},
year={2005},
month={Dec},
day={01},
volume={121},
number={5},
pages={823-841},
issn={1572-9613},
doi={10.1007/s10955-005-8666-6},
url={https://doi.org/10.1007/s10955-005-8666-6}
}


@article{DS98,
    author = {Sreenivasan, Katepalli R. and Dhruva, Brindesh},
    title = "{Is There Scaling in High-Reynolds-Number Turbulence?}",
    journal = {Progress of Theoretical Physics Supplement},
    volume = {130},
    pages = {103-120},
    year = {1998},
    month = {01},
    issn = {0375-9687},
    doi = {10.1143/PTPS.130.103},
    url = {https://doi.org/10.1143/PTPS.130.103},
}
%    eprint = {https://academic.oup.com/ptps/article-pdf/doi/10.1143/PTPS.130.103/5211940/130-103.pdf},

@article{Y07,
	doi = {10.1088/1367-2630/9/4/089},
	url = {https://doi.org/10.1088%2F1367-2630%2F9%2F4%2F089},
	year = 2007,
	month = {apr},
	publisher = {{IOP} Publishing},
	volume = {9},
	number = {4},
	pages = {89--89},
	author = {Jörg Schumacher and Katepalli R Sreenivasan and Victor Yakhot},
	title = {Asymptotic exponents from low-Reynolds-number flows},
	journal = {New Journal of Physics}
}

@article{Y14,
  title = {Reynolds number of transition and self-organized criticality of strong turbulence},
  author = {Yakhot, Victor},
  journal = {Phys. Rev. E},
  volume = {90},
  issue = {4},
  pages = {043019},
  numpages = {8},
  year = {2014},
  month = {Oct},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevE.90.043019},
  url = {https://link.aps.org/doi/10.1103/PhysRevE.90.043019}
}
@Article{She1990,
author={She, Zhen-Su
and Jackson, Eric
and Orszag, Steven A.},
title={Intermittent vortex structures in homogeneous isotropic turbulence},
journal={Nature},
year={1990},
month={Mar},
day={01},
volume={344},
number={6263},
pages={226-228},
issn={1476-4687},
doi={10.1038/344226a0},
url={https://doi.org/10.1038/344226a0}
}


@article{Buaria_2019,
	doi = {10.1088/1367-2630/ab0756},
	url = {https://doi.org/10.1088%2F1367-2630%2Fab0756},
	year = 2019,
	month = {apr},
	publisher = {{IOP} Publishing},
	volume = {21},
	number = {4},
	pages = {043004},
	author = {Dhawal Buaria and Alain Pumir and Eberhard Bodenschatz and P K Yeung},
	title = {Extreme velocity gradients in turbulent flows},
	journal = {New Journal of Physics}
}
@article{ISY20,
  title = {Scaling exponents saturate in three-dimensional isotropic turbulence},
  author = {Iyer, Kartik P. and Sreenivasan, Katepalli R. and Yeung, P. K.},
  journal = {Phys. Rev. Fluids},
  volume = {5},
  issue = {5},
  pages = {054605},
  numpages = {16},
  year = {2020},
  month = {May},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevFluids.5.054605},
  url = {https://link.aps.org/doi/10.1103/PhysRevFluids.5.054605}
}

@article{KM80,
    title = "On the topological meaning of canonical Clebsch variables",
    journal = "Physics Letters A",
    volume = "77",
    number = "1",
    pages = "37 - 38",
    year = "1980",
    issn = "0375-9601",
    doi = "https://doi.org/10.1016/0375-9601(80)90627-1",
    url = "http://www.sciencedirect.com/science/article/pii/0375960180906271",
    author = "E.A. Kuznetsov and A.V. Mikhailov"
}

@misc{M19a,
    Author = {Alexander Migdal},
    Title = {Universal Area Law in Turbulence},
    Year = {2019},
    archivePrefix={arXiv},
    eprint = {arXiv:1903.08613},
    url = {https://arxiv.org/abs/1903.08613}
}

@misc{M19b,
    Author = {Alexander Migdal},
    Title = {Scaling Index $\alpha = \frac{1}{2}$ In Turbulent Area Law},
    Year = {2019},
    archivePrefix={arXiv},
    eprint = {arXiv:1904.00900v2},
    url = {https://arxiv.org/abs/1904.00900v2}
}

@misc{M19c,
    Author = {Alexander Migdal},
    Title = {Exact Area Law for Planar Loops in Turbulence in Two and Three Dimensions},
    Year = {2019},
    archivePrefix={arXiv},
    eprint = {arXiv:1904.05245v2},
    url = {https://arxiv.org/abs/1904.05245v2}
}

@misc{M19d,
    Author = {Alexander Migdal},
    Title = {Analytic and Numerical Study of Navier-Stokes Loop Equation in Turbulence},
    Year = {2019},
    archivePrefix={arXiv},
    eprint = {arXiv:1908.01422v1},
    url = {https://arxiv.org/abs/1908.01422v1}
}

@misc{M19e,
    Author = {Alexander Migdal},
    Title = {Turbulence, String Theory and Ising Model},
    Year = {2019},
    archivePrefix={arXiv},
    eprint = {arXiv:1912.00276v3},
    url = {https://arxiv.org/abs/1912.00276v3}
}

@misc{M20a,
    title={Towards Field Theory of Turbulence},
    author={Alexander Migdal},
    year={2020},
    eprint={2005.01231},
    archivePrefix={arXiv},
    primaryClass={hep-th},
    url = {https://arxiv.org/abs/2005.01231}
}
@misc{M20b,
    title={Probability Distribution of Velocity Circulation in Three Dimensional Turbulence},
    author={Alexander Migdal},
    year={2020},
    eprint={2006.12008},
    archivePrefix={arXiv},
    primaryClass={hep-th},
    url = {https://arxiv.org/abs/2006.12008}
}
@article{BMO84,
title = {Boundary integral methods for axisymmetric and three-dimensional Rayleigh-Taylor instability problems},
journal = {Physica D: Nonlinear Phenomena},
volume = {12},
number = {1},
pages = {19-31},
year = {1984},
issn = {0167-2789},
doi = {https://doi.org/10.1016/0167-2789(84)90511-6},
url = {https://www.sciencedirect.com/science/article/pii/0167278984905116},
author = {Gregory R. Baker and Daniel I. Meiron and Steven A. Orszag}
}
@article{M20c,
  doi = {10.1142/s0217751x20300185},
  url = {https://doi.org/10.1142/s0217751x20300185},
  year = {2020},
  month = {nov},
  publisher = {World Scientific Pub Co Pte Lt},
  volume = {35},
  number = {31},
  pages = {2030018},
  author = {Alexander Migdal},
  title = {Clebsch confinement and instantons in turbulence},
  journal = {International Journal of Modern Physics A},
   eprint={2007.12468v7},
    archivePrefix={arXiv},
    primaryClass={hep-th}
}

@article{Tubes19,
	doi = {10.1088/1367-2630/ab0756},
	url = {https://doi.org/10.1088/1367-2630/ab0756},
	year = 2019,
	month = {apr},
	publisher = {{IOP} Publishing},
	volume = {21},
	number = {4},
	pages = {043004},
	author = {Dhawal Buaria and Alain Pumir and Eberhard Bodenschatz and P K Yeung},
	title = {Extreme velocity gradients in turbulent flows},
	journal = {New Journal of Physics},
	abstract = {Fully turbulent flows are characterized by intermittent formation of very localized and intense velocity gradients. These gradients can be orders of magnitude larger than their typical value and lead to many unique properties of turbulence. Using direct numerical simulations of the Navier–Stokes equations with unprecedented small-scale resolution, we characterize such extreme events over a significant range of turbulence intensities, parameterized by the Taylor-scale Reynolds number (). Remarkably, we find the strongest velocity gradients to empirically scale as , with , where is the Kolmogorov time scale (with its inverse, , being the rms of velocity gradient fluctuations). Additionally, we observe velocity increments across very small distances , where η is the Kolmogorov length scale, to be as large as the rms of the velocity fluctuations. Both observations suggest that the smallest length scale in the flow behaves as , with , which is at odds with predictions from existing phenomenological theories. We find that extreme gradients are arranged in vortex tubes, such that strain conditioned on vorticity grows on average slower than vorticity, approximately as a power law with an exponent , which weakly increases with . Using scaling arguments, we get , which suggests that β would also slowly increase with . We conjecture that approaching the mathematical limit of infinite , strain and vorticity would scale similarly resulting in and hence extreme events occurring at a scale corresponding to .}
}

@article{VortexGasCirculation20,
author = {Apolinario, Gabriel and Moriconi, Luca and Pereira, Rodrigo and valadão, Victor},
year = {2020},
month = {10},
pages = {041102},
title = {Vortex Gas Modeling of Turbulent Circulation Statistics},
volume = {102},
journal = {PHYSICAL REVIEW E},
doi = {10.1103/PhysRevE.102.041102}
}

@article{QuantumCirculation21,
  title = {Intermittency of Velocity Circulation in Quantum Turbulence},
  author = {M\"uller, Nicol\'as P. and Polanco, Juan Ignacio and Krstulovic, Giorgio},
  journal = {Phys. Rev. X},
  volume = {11},
  issue = {1},
  pages = {011053},
  numpages = {13},
  year = {2021},
  month = {Mar},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevX.11.011053},
  url = {https://link.aps.org/doi/10.1103/PhysRevX.11.011053}
}



@misc{ADS,
   author = "Wikipedia",
   title = "{AdS-CFT correspondence} --- {W}ikipedia{,} The Free Encyclopedia",
   year = "2019",
   howpublished = {\url{https://en.wikipedia.org/wiki/AdS/CFT_correspondence}},
   note = "[Online; accessed 28-October-2021]"
}
@article{M21a,
author = {Migdal,Alexander },
title = {Asymmetric vortex sheet},
journal = {Physics of Fluids},
volume = {33},
number = {3},
pages = {035127},
year = {2021},
doi = {10.1063/5.0044724},

URL = { 
        https://doi.org/10.1063/5.0044724
    
},
eprint = { 
        https://doi.org/10.1063/5.0044724
    
}

}




@article{M21b,
author = {Migdal, Alexander},
title = {Vortex sheet turbulence as solvable string theory},
journal = {International Journal of Modern Physics A},
volume = {36},
number = {05},
pages = {2150062},
year = {2021},
doi = {10.1142/S0217751X21500627},

URL = { 
        https://doi.org/10.1142/S0217751X21500627
    
},
eprint = { 
        https://doi.org/10.1142/S0217751X21500627
    
}
,
    abstract = { We study steady vortex sheet solutions of the Navier–Stokes in the limit of vanishing viscosity at fixed energy flow. We refer to this as the turbulent limit. These steady flows correspond to a minimum of the Euler Hamiltonian as a functional of the tangent discontinuity of the local velocity parametrized as Δv→t = ∇→Γ. This observation means that the steady flow represents the low-temperature limit of the Gibbs distribution for vortex sheet dynamics with the normal displacement δr⊥ of the vortex sheet as a Hamiltonian coordinate and Γ as a conjugate momentum. An infinite number of Euler conservation laws lead to a degenerate vacuum of this system, which explains the complexity of turbulence statistics and provides the relevant degrees of freedom (random surfaces). The simplest example of a steady solution of the Navier–Stokes equation in the turbulent limit is a spherical vortex sheet whose flow outside is equivalent to a potential flow past a sphere, while the velocity is constant inside the sphere. Potential flow past other bodies provide other steady solutions. The new ingredient we add is a calculable gap in tangent velocity, leading to anomalous dissipation. This family of steady solutions provides an example of the Euler instanton advocated in our recent work, which is supposed to be responsible for the dissipation of the Navier–Stokes equation in the turbulent limit. We further conclude that one can obtain turbulent statistics from the Gibbs statistics of vortex sheets by adding Lagrange multipliers for the conserved volume inside closed surfaces, the rate of energy pumping, and energy dissipation. The effective temperature in our Gibbs distribution goes to zero as Re− 1 3 with Reynolds number Re ∼ ν− 6 5 in the turbulent limit. The Gibbs statistics in this limit reduces to the solvable string theory in two dimensions (so-called c = 1 critical matrix model). This opens the way for nonperturbative calculations in the Vortex Sheet Turbulence, some of which we report here. }
}


@misc{M21c,
      title={Confined Vortex Surface and Irreversibility. 1. Properties of Exact solution}, 
      author={Alexander Migdal},
      year={2021},
      eprint={2103.02065v10},
      archivePrefix={arXiv},
      primaryClass={physics.flu-dyn},
      url = {https://doi.org/10.1142/S0217751X21500974}
}

@misc{M21d,
      title={Confined Vortex Surface and Irreversibility. 2. Hyperbolic Sheets and Turbulent statistics}, 
      author={Alexander Migdal},
      year={2021},
      eprint={2105.12719},
      archivePrefix={arXiv},
      primaryClass={physics.flu-dyn},
      url = {https://arxiv.org/abs/2105.12719}
}

@article{M22,
    author ={  Alexander Migdal},
    year ={2023},
    title = {Vortex lines, anomalous dissipation, and intermittency},
    journal = {Physics of Fluids},
    eprint={2212.13356},
      archivePrefix={arXiv},
      primaryClass={physics.flu-dyn},
      url = {https://arxiv.org/abs/2105.12719}
}
@article{M23PR,
  doi = {10.48550/ARXIV.2209.12312},
  eprint={2209.12312},
      archivePrefix={arXiv},
      primaryClass={physics.flu-dyn},
      url = {https://arxiv.org/abs/2209.12312},
  
  author = {Migdal, Alexander},
  
  keywords = {Fluid Dynamics (physics.flu-dyn), High Energy Physics - Theory (hep-th), Mathematical Physics (math-ph), Chaotic Dynamics (nlin.CD), Pattern Formation and Solitons (nlin.PS), FOS: Physical sciences, FOS: Physical sciences},
  
  title = {Statistical Equilibrium of Circulating Fluids},
  year = {2023},
  volume= {1011C},
   pages={1-117},
   journal = {Physics Reports},
  copyright = {Creative Commons Zero v1.0 Universal}
  
}


@article{KS21,
    author = {Shariff,Karim  and Elsinga,Gerrit E. },
    title = {Viscous vortex layers subject to more general strain and comparison to isotropic turbulence},
    journal = {Physics of Fluids},
    volume = {33},
    number = {3},
    pages = {033611},
    year = {2021},
    doi = {10.1063/5.0045243},
    
    URL = { 
            https://doi.org/10.1063/5.0045243
        
    },
    eprint = { 
            https://doi.org/10.1063/5.0045243
    }

}

@article{Sreeni84,
author = {Sreenivasan,K. R. },
title = {On the scaling of the turbulence energy dissipation rate},
journal = {The Physics of Fluids},
volume = {27},
number = {5},
pages = {1048-1051},
year = {1984},
doi = {10.1063/1.864731},

URL = { 
        https://aip.scitation.org/doi/abs/10.1063/1.864731
    
},
eprint = { 
        https://aip.scitation.org/doi/pdf/10.1063/1.864731
    
}

}

@article{S19,
  title = {Circulation in High Reynolds Number Isotropic Turbulence is a Bifractal},
  author = {Iyer, Kartik P. and Sreenivasan, Katepalli R. and Yeung, P. K.},
  journal = {Phys. Rev. X},
  volume = {9},
  issue = {4},
  pages = {041006},
  numpages = {13},
  year = {2019},
  month = {Oct},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevX.9.041006},
  url = {https://link.aps.org/doi/10.1103/PhysRevX.9.041006}
}


@article{L81,
  title={The Hamiltonian formulation of the Euler equation and subsequent constraints on the properties of randomly stirred fluids},
  author={Levich, E},
  journal={Physics Letters A},
  volume={86},
  number={3},
  pages={165--168},
  year={1981},
  publisher={Elsevier}
}
@article{M83,
    title = "Coadjoint orbits, vortices, and Clebsch variables for incompressible fluids",
    journal = "Physica D: Nonlinear Phenomena",
    volume = "7",
    number = "1",
    pages = "305 - 323",
    year = "1983",
    issn = "0167-2789",
    doi = "https://doi.org/10.1016/0167-2789(83)90134-3",
    url = "http://www.sciencedirect.com/science/article/pii/0167278983901343",
    author = "Jerrold Marsden and Alan Weinstein",
}

@inproceedings{TSVS,
    title={Turbulence as Statistics of Vortex Cells},
    author={A. A. Migdal},
    year={1993},
    eprint={hep-th/9306152v2},
    archivePrefix={arXiv},
    primaryClass={hep-th},
    pages = {178--204},
    url = {https://arxiv.org/abs/hep-th/9306152v2},
    booktitle={The First Landau Institute Summer School, 1993: Selected Proceedings},
    editor={Mineev, V.P.},
    isbn={9782884491389},
    lccn={95223553},
    bookyear={1995},
    publisher={Gordon and Breach},
}

@article{KPZ,
author = {Knizhnik, V.G. and Polyakov, A.M. and Zamolodchikov, A.B.},
title = {FRACTAL STRUCTURE OF 2d—QUANTUM GRAVITY},
journal = {Modern Physics Letters A},
volume = {03},
number = {08},
pages = {819-826},
year = {1988},
doi = {10.1142/S0217732388000982},
URL = { https://doi.org/10.1142/S0217732388000982},
eprint = {https://doi.org/10.1142/S0217732388000982}
}

@article{Pol81,
    author = "Polyakov, Alexander M.",
    editor = "Khalatnikov, I.M. and Mineev, V.P.",
    title = "{Quantum Geometry of Bosonic Strings}",
    reportNumber = "Print-81-0351 (LANDAU INST)",
    doi = "10.1016/0370-2693(81)90743-7",
    journal = "Phys. Lett. B",
    volume = "103",
    pages = "207--210",
    year = "1981"
}

@article{DK81,
    author = "Distler, Jacques and Kawai, Hikaru",
    title = "{Conformal Field Theory and 2D Quantum Gravity}",
    reportNumber = "CLNS-88-853",
    doi = "10.1016/0550-3213(89)90354-4",
    journal = "Nucl. Phys. B",
    volume = "321",
    pages = "509--527",
    year = "1989"
}
@article{Novikov_1993,
	doi = {10.1016/0169-5983(93)90108-m},
	url = {https://doi.org/10.1016%2F0169-5983%2893%2990108-m},
	year = 1993,
	month = {aug},
	publisher = {{IOP} Publishing},
	volume = {12},
	number = {2},
	pages = {107--126},
	author = {E Novikov},
	title = {A new approach to the problem of turbulence, based on the conditionally averaged Navier-Stokes equations},
	journal = {Fluid Dynamics Research}
	}
@misc{FP,
   author = "Wikipedia",
   title = "{Fundamental polygon} --- {W}ikipedia{,} The Free Encyclopedia",
   year = "2019",
   howpublished = {\url{http://en.wikipedia.org/w/index.php?title=Fundamental_polygon}},
   note = "[Online; accessed 29-November-2019]"
}
@misc{VR,
   author = "Wikipedia",
   title = "{Vortex ring} --- {W}ikipedia{,} The Free Encyclopedia",
   year = "2020",
   howpublished = {\url{https://en.wikipedia.org/wiki/Vortex_ring}},
   note = "[Online; accessed 07-October-2020]"
}
@misc{EW,
    author = "Wikipedia",
    title= "{Weierstrass–Enneper parameterization}",
    year ="2019",
    howpublished = {\url{https://en.wikipedia.org/wiki/Weierstrass\%E2\%80\%93Enneper_parameterization}},
    note = "[Online; accessed 13-December-2019]"
}


@misc{RSM,
    author = "Wikipedia",
    title= "{Random Matrix}",
    year ="2021",
    howpublished = {\url{https://en.wikipedia.org/wiki/Random_matrix}},
    note = "[Online; accessed 30-September-2021]"
}
@misc{SVD,
    author = "Wikipedia",
    title="{Singular Value Decomposition}",
    year ="2020",
    howpublished = {\url{https://en.wikipedia.org/wiki/Singular_value_decomposition}},
     note = "[Online; accessed 20-June-2020]"
}

@misc{BurgersVortex,
    author = "Wikipedia",
    title="{Burgers vortex}",
    year ="2022",
    howpublished = {\url{https://en.wikipedia.org/wiki/Burgers_vortex}},
     note = "[Online; accessed 27-April-2022]"
}


@article{VTubes,
author = {Ishihara, Takashi and Gotoh, Toshiyuki and Kaneda, Yukio},
year = {2008},
month = {12},
pages = {165-180},
title = {Study of High–Reynolds Number Isotropic Turbulence by Direct Numerical Simulation},
volume = {41},
journal = {Annual Review of Fluid Mechanics},
doi = {10.1146/annurev.fluid.010908.165203}
}
@book{Lamb45,
  title={Hydrodynamics},
  author={Lamb, H.},
  year={1945},
  publisher={Dover publications},
  isbn={9780486602561},
  lccn={lc46001891},
  url={https://books.google.com/books?id=237xDg7T0RkC},
}

@article{FKLM,
  title = {Instantons and intermittency},
  author = {Falkovich, G. and Kolokolov, I. and Lebedev, V. and Migdal, A.},
  journal = {Phys. Rev. E},
  volume = {54},
  issue = {5},
  pages = {4896--4907},
  numpages = {0},
  year = {1996},
  month = {Nov},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevE.54.4896},
  url = {https://link.aps.org/doi/10.1103/PhysRevE.54.4896}
}

@misc{MLE2019,
    author = {Alexander Migdal},
    title  = {Loop Equation},
    url = {https://www.wolframcloud.com/obj/sasha.migdal/Published/LoopEquation.nb}
}


@misc{Klebanov91,
    Author = {Igor Klebanov},
    Title = {String Theory in Two Dimensions},
    Year = {1991},
    eprint = {arXiv:hep-th/9108019v2},
    url = {https://arxiv.org/abs/hep-th/9108019v2}
}
@article{YZ93,
title = "Hidden conservation laws in hydrodynamics; energy and dissipation rate fluctuation spectra in strong turbulence",
journal = "Physica D: Nonlinear Phenomena",
volume = "64",
number = "4",
pages = "379 - 394",
year = "1993",
issn = "0167-2789",
doi = "https://doi.org/10.1016/0167-2789(93)90050-B",
url = "http://www.sciencedirect.com/science/article/pii/016727899390050B",
author = "Victor Yakhot and Vladimir Zakharov"
}


@article{khalat52,
  title={The hydrodynamics of solutions of impurities in helium II},
  author={Khalatnikov, I.M.},
  journal={Zh. Eksp. Teor. Fiz},
  volume={23},
  pages={169},
  year={1952}
}

@article{YS04,
title = "Towards a dynamical theory of multifractals in turbulence",
journal = "Physica A: Statistical Mechanics and its Applications",
volume = "343",
pages = "147 - 155",
year = "2004",
issn = "0378-4371",
doi = "https://doi.org/10.1016/j.physa.2004.07.037",
url = "http://www.sciencedirect.com/science/article/pii/S0378437104010593",
author = "Victor Yakhot and K.R. Sreenivasan",
keywords = "Turbulence, Dynamical systems"
}

@article{KR73, title={Helical turbulence and absolute equilibrium}, volume={59}, DOI={10.1017/S0022112073001837}, number={4}, journal={Journal of Fluid Mechanics}, publisher={Cambridge University Press}, author={Kraichnan, Robert H.}, year={1973}, pages={745–752}}

@misc{M89,
    author = {Alexander Migdal},
    title = {Fractal Dimension of Vorticity},
    year = {1989},
    note = {Talk at ACM seminar in Princeton University}
}
@misc{S17,
author = {Iyer, Kartik P. and Sreenivasan, Katepalli R. and Yeung, P. K.},
  title = {On the non-linear amplification in
 hydrodynamic turbulence},
  year = {2017},
  note = { To be published}
}

@article{SK20,
  title = {Scaling exponents saturate in three-dimensional isotropic turbulence},
  author = {Iyer, Kartik P. and Sreenivasan, Katepalli R. and Yeung, P. K.},
  journal = {Phys. Rev. Fluids},
  volume = {5},
  issue = {5},
  pages = {054605},
  numpages = {16},
  year = {2020},
  month = {May},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevFluids.5.054605},
  url = {https://link.aps.org/doi/10.1103/PhysRevFluids.5.054605}
}

@Article{KI13,
author={Kleckner, Dustin
and Irvine, William T. M.},
title={Creation and dynamics of knotted vortices},
journal={Nature Physics},
year={2013},
month={Apr},
day={01},
volume={9},
number={4},
pages={253-258},
issn={1745-2481},
doi={10.1038/nphys2560},
url={https://doi.org/10.1038/nphys2560}
}
@article{MO69, title={The degree of knottedness of tangled vortex lines}, volume={35}, DOI={10.1017/S0022112069000991}, number={1}, journal={Journal of Fluid Mechanics}, publisher={Cambridge University Press}, author={Moffatt, H. K.}, year={1969}, pages={117–129}}

@misc{IM19,
    author = {T. Matsuzawa and W. Irvine},
    title = {Realization of Confined Turbulence Through Multiple Vortex Ring Collisions},
    year = {03/12/2019},
    note = {"Talk at the Flatiron Conference Universality Turbulence Across Vast Scales"},
    eprint={https://www.quantamagazine.org/an-unexpected-twist-lights-up-the-secrets-of-turbulence-20200903/}

}
@misc{IMS20,
    author = { Kartik Iyer,  Alexander Migdal   and Katepalli Sreenivasan},
    title = {?},
    year = {2020},
    note = {To be submitted to arXiv}
}
@article{GPR94,
title = "Target space duality in string theory",
journal = "Physics Reports",
volume = "244",
number = "2",
pages = "77 - 202",
year = "1994",
issn = "0370-1573",
doi = "https://doi.org/10.1016/0370-1573(94)90070-1",
url = "http://www.sciencedirect.com/science/article/pii/0370157394900701",
author = "Amit Giveon and Massimo Porrati and Eliezer Rabinovici"
}

@Article{AMV86,
author="Alvarez-Gaum{\'e}, Luis
and Moore, Gregory
and Vafa, Cumrun",
title="Theta functions, modular invariance, and strings",
journal="Communications in Mathematical Physics",
year="1986",
month="Mar",
day="01",
volume="106",
number="1",
pages="1--40"
}

@Article{Ta01,
author="Takhtajan, Leon A.",
title="Free Bosons and Tau-Functions for Compact Riemann Surfaces and Closed Smooth Jordan Curves. Current Correlation Functions",
journal="Letters in Mathematical Physics",
year="2001",
month="Jun",
day="01",
volume="56",
number="3",
pages="181--228",
issn="1573-0530",
doi="10.1023/A:1017999407650",
url="https://doi.org/10.1023/A:1017999407650"
}

@article{Ishihara88,
author = {Ishihara, Takashi and Gotoh, Toshiyuki and Kaneda, Yukio},
year = {2008},
month = {12},
pages = {165-180},
title = {Study of High–Reynolds Number Isotropic Turbulence by Direct Numerical Simulation},
volume = {41},
journal = {Annual Review of Fluid Mechanics},
doi = {10.1146/annurev.fluid.010908.165203}
}

@misc{IBS20,
    title={Area rule for circulation and minimal surfaces in three-dimensional turbulence},
    author={Kartik P. Iyer and Sachin S. Bharadwaj and Katepalli R. Sreenivasan},
    year={2020},
    eprint={2007.06723},
    archivePrefix={arXiv},
    primaryClass={physics.flu-dyn}
}

@article{GM96,
  title = {Instantons in the Burgers equation},
  author = {Gurarie, Victor and Migdal, Alexander},
  journal = {Phys. Rev. E},
  volume = {54},
  issue = {5},
  pages = {4908--4914},
  year = {1996},
  month = {Nov},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevE.54.4908},
  url = {https://link.aps.org/doi/10.1103/PhysRevE.54.4908}
}


@article{SZ89,
  title = {The large-scale structure of the universe: Turbulence, intermittency, structures in a self-gravitating medium},
  author = {Shandarin, S. F. and Zeldovich, Ya. B.},
  journal = {Rev. Mod. Phys.},
  volume = {61},
  issue = {2},
  pages = {185--220},
  numpages = {0},
  year = {1989},
  month = {Apr},
  publisher = {American Physical Society},
  doi = {10.1103/RevModPhys.61.185},
  url = {https://link.aps.org/doi/10.1103/RevModPhys.61.185}
}

@article{Genz91,
author = {Berntsen, Jarle and Espelid, Terje O. and Genz, Alan},
title = {An Adaptive Algorithm for the Approximate Calculation of Multiple Integrals},
year = {1991},
issue_date = {Dec. 1991},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
volume = {17},
number = {4},
issn = {0098-3500},
url = {https://doi.org/10.1145/210232.210233},
doi = {10.1145/210232.210233},
journal = {ACM Trans. Math. Softw.},
month = dec,
pages = {437–451},
numpages = {15}
}

@misc{cubature,
    author = {Steven Johnson},
    title  = {Cubature (Multi-dimensional integration)},
    year = {2017},
    month = {Jul},
    url = {http://ab-initio.mit.edu/wiki/index.php/Cubature_(Multi-dimensional_integration)}
}
@misc{MB,
    howpublished={https://www.wolframcloud.com/obj/sasha.migdal/Published/BurgersSolutionNavierStokes.nb},
    author = {Alexander Migdal},
    title= {Burgers Vortex Sheet Solution of the Navier-Stokes Equation.},
    year = {2021},
    month = {Feb}
}
@misc{MB3,
    howpublished={https://www.wolframcloud.com/obj/sasha.migdal/Published/MatrixIntegrals.nb},
    author = {Alexander Migdal},
    title= {Matrix Integrals},
    year = {2022},
    month = {September}
}
@misc{MB4,
    howpublished={https://www.wolframcloud.com/obj/sasha.migdal/Published/ComputattionsForMasterEquationOnaSphere.nb},
    author = {Alexander Migdal},
    title= {Computations For Master Equation On a Sphere},
    year = {2021},
    month = {Mar}
}

@misc{MB5,
    howpublished={https://www.wolframcloud.com/obj/sasha.migdal/Published/CVSGammaOnSphereHarmonicsExpansion.nb},
    author = {Alexander Migdal},
    title= {Symmetric Confined Vortex Surface. Gamma Legendre Expansion.},
    year = {2021},
    month = {Feb}
}

@misc{MB7,
    howpublished={https://www.wolframcloud.com/obj/sasha.migdal/Published/GenericCylindricVortexSheet.nb},
    author = {Alexander Migdal},
    title= {Generic Cylindric Vortex Sheet},
    year = {2021},
    month = {Mar}
}

@misc{MB8,
    howpublished={https://www.wolframcloud.com/obj/sasha.migdal/Published/NDimensionalTensorMath.nb},
    author = {Alexander Migdal},
    title= {N dimensional Tensor algebra and Gradients},
    year = {2021},
    month = {Mar}
}



@book{BAT00, 
publisher={Cambridge University Press},
author={Batchelor, G. K.},
title={An Introduction to Fluid Dynamics},
year={2000}, 
DOI={10.1017/CBO9780511800955}, 
collection={Cambridge Mathematical Library}
}

@misc{MinSurfaceX,
author ={Henrik Schumacher  Beltukov, Rahul},
title ="{ Can Mathematica solve Plateau's problem (finding a minimal surface with specified boundary)?}", 
year = 2022,
url = {https://mathematica.stackexchange.com/questions/72203/can-mathematica-solve-plateaus-problem-finding-a-minimal-surface-with-specified boundary}
}

@misc{Stagnation,
   author = "Wikipedia",
   title = "{Stagnation point flow} --- {W}ikipedia{,} The Free Encyclopedia",
   year = "2021",
   url = {https://en.wikipedia.org/wiki/Stagnation_point_flow},
   note = "[Online; accessed 24-January-2021]"
}
@misc{MB9,
    howpublished={https://www.wolframcloud.com/obj/sasha.migdal/Published/ExactAsymmetricVortexSheet.nb},
    author = {Alexander Migdal},
    title= {Exact Asymmetric Vortex Sheet},
    year = {2021},
    month = {Apr}
}

@misc{MB10,
    howpublished={https://www.wolframcloud.com/obj/sasha.migdal/Published/BurgersVortexWithNormalShock.nb},
    author = {Alexander Migdal},
    title= {Burgers Vortex With Normal Shock},
    year = {2021},
    month = {Apr}
}


@misc{MB11,
    howpublished={https://www.wolframcloud.com/obj/sasha.migdal/Published/ExactAlgebraicCVS.nb},
    author = {Alexander Migdal},
    title= {Exact Algebraic CVS},
    year = {2021},
    month = {May}
}

@misc{MB12,
    howpublished={https://www.wolframcloud.com/obj/sasha.migdal/Published/SolutionCVSForCylinder.nb},
    author = {Alexander Migdal},
    title= {Strained Circular Tube},
    year = {2021},
    month = {Apr}
}

@misc{MB13,
    howpublished={https://www.wolframcloud.com/obj/sasha.migdal/Published/RGP.nb},
    author = {Alexander Migdal},
    title= {Riemann-Hilbert Problem},
    year = {2021},
    month = {May}
}



@misc{MB14,
    howpublished={https://www.wolframcloud.com/obj/sasha.migdal/Published/AlgebraicCVS.nb},
    author = {Alexander Migdal},
    title= {Algebraic CVS},
    year = {2021},
    month = {August}
}

@misc{MB15,
    howpublished={https://www.wolframcloud.com/obj/sasha.migdal/Published/HyperbolicFlow.nb},
    author = {Alexander Migdal},
    title= {Hyperbolic Flow},
    year = {2021},
    month = {August}
}

@misc{MB16,
    howpublished={https://www.wolframcloud.com/obj/sasha.migdal/Published/GeneralVortexSheet.nb},
    author = {Alexander Migdal},
    title= {General Vortex Sheet},
    year = {2021},
    month = {August}
}



@misc{MB17,
    howpublished={https://www.wolframcloud.com/obj/sasha.migdal.gmail/Published/ClosedCVS.nb},
    author = {Alexander Migdal},
    title= {Closed CVS},
    year = {2021},
    month = {October}
}

@misc{MB18,
    howpublished={https://www.wolframcloud.com/obj/sasha.migdal\\
    /Published/VectorPlotClebsch.nb},
    author = {Alexander Migdal},
    title= {Vector Plot of Kelvinon Vorticity},
    year = {2023},
    month = {Mar}
}

@misc{BrT,
 author = "Wikipedia",
    title="{Brouwer Fixed-point Theorem}",
    year ="2021",
    howpublished = {\url{https://en.wikipedia.org/wiki/Brouwer_fixed-point_theorem}},
     note = "[Online; accessed 11-June-2021]"
}

@article{SreeniDissipation,
author = {Sreenivasan,K. R. },
title = {On the scaling of the turbulence energy dissipation rate},
journal = {The Physics of Fluids},
volume = {27},
number = {5},
pages = {1048-1051},
year = {1984},
doi = {10.1063/1.864731},

URL = { 
        https://aip.scitation.org/doi/abs/10.1063/1.864731
    
},
eprint = { 
        https://aip.scitation.org/doi/pdf/10.1063/1.864731
    
}

}


@article {S21,
	Title = {The area rule for circulation in three-dimensional turbulence},
	Author = {Iyer, Kartik P and Bharadwaj, Sachin S and Sreenivasan, Katepalli R},
	DOI = {10.1073/pnas.2114679118},
	Number = {43},
	Volume = {118},
	Month = {October},
	Year = {2021},
	Journal = {Proceedings of the National Academy of Sciences of the United States of America},
	ISSN = {0027-8424},
	Pages = {e2114679118},
	URL = {https://europepmc.org/articles/PMC8639329},
}

@article{SY21,
  title = {Dynamics of three-dimensional turbulence from Navier-Stokes equations},
  author = {Sreenivasan, Katepalli R. and Yakhot, Victor},
  journal = {Phys. Rev. Fluids},
  volume = {6},
  issue = {10},
  pages = {104604},
  numpages = {21},
  year = {2021},
  month = {Oct},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevFluids.6.104604},
  url = {https://link.aps.org/doi/10.1103/PhysRevFluids.6.104604}
}

@misc{SY22,
  doi = {10.48550/ARXIV.2208.09561},
  
  url = {https://arxiv.org/abs/2208.09561},
  
  author = {Sreenivasan, Katepalli R. and Yakhot, Victor},
  
  keywords = {Fluid Dynamics (physics.flu-dyn), Statistical Mechanics (cond-mat.stat-mech), Applied Physics (physics.app-ph), FOS: Physical sciences, FOS: Physical sciences},
  
  title = {The saturation of exponents and the asymptotic fourth state of turbulence},
  
  publisher = {arXiv},
  
  year = {2022},
  
  copyright = {arXiv.org perpetual, non-exclusive license}
}

@article{VortStrain87,
author = {Ashurst,Wm. T.  and Kerstein,A. R.  and Kerr,R. M.  and Gibson,C. H. },
title = {Alignment of vorticity and scalar gradient with strain rate in simulated Navier–Stokes turbulence},
journal = {The Physics of Fluids},
volume = {30},
number = {8},
pages = {2343-2353},
year = {1987},
doi = {10.1063/1.866513},

URL = { 
        https://aip.scitation.org/doi/abs/10.1063/1.866513
    
},
eprint = { 
        https://aip.scitation.org/doi/pdf/10.1063/1.866513
    
}

}
@article{PosFunc,
 ISSN = {00255718, 10886842},
 URL = {http://www.jstor.org/stable/2153721},
 abstract = {In this paper we study strictly positive definite functions on the unit sphere of the m-dimensional Euclidean space. Such functions can be used for solving a scattered data interpolation problem on spheres. Since positive definite functions on the sphere were already characterized by Schoenberg some fifty years ago, the issue here is to determine what kind of positive definite functions are actually strictly positive definite. The study of this problem was initiated recently by Xu and Cheney (Proc. Amer. Math. Soc. 116 (1992), 977-981), where certain sufficient conditions were derived. A new approach, which is based on a critical connection between this problem and that of multivariate polynomial interpolation on spheres, is presented here. The relevant interpolation problem is subsequently analyzed by three different complementary methods. The first is based on the de Boor-Ron general "least solution for the multivariate polynomial interpolation problem". The second, which is suitable only for m = 2, is based on the connection between bivariate harmonic polynomials and univariate analytic polynomials, and reduces the problem to the structure of the integer zeros of bounded univariate exponentials. Finally, the last method invokes the realization of harmonic polynomials as the polynomial kernel of the Laplacian, thereby exploiting some basic relations between homogeneous ideals and their polynomial kernels.},
 author = {Amos Ron and Xingping Sun},
 journal = {Mathematics of Computation},
 number = {216},
 pages = {1513--1530},
 publisher = {American Mathematical Society},
 title = {Strictly Positive Definite Functions on Spheres in Euclidean Spaces},
 volume = {65},
 year = {1996}
}


@Article{LKQ19,
AUTHOR = {Lei, Kin and Qi, Dongxu and Tian, Xiaolin},
TITLE = {A New Coordinate System for Constructing Spherical Grid Systems},
JOURNAL = {Applied Sciences},
VOLUME = {10},
YEAR = {2020},
NUMBER = {2},
ARTICLE-NUMBER = {655},
URL = {https://www.mdpi.com/2076-3417/10/2/655},
ISSN = {2076-3417},
ABSTRACT = {In astronomy, physics, climate modeling, geoscience, planetary science, and many other disciplines, the mass of data often comes from spherical sampling. Therefore, establishing an efficient and distortion-free representation of spherical data is essential. This paper introduces a novel spherical (global) coordinate system that is free of singularity. Contrary to classical coordinates, such as Cartesian or spherical polar systems, the proposed coordinate system is naturally defined on the spherical surface. The basic idea of this coordinate system originated from the classical planar barycentric coordinates that describe the positions of points on a plane concerning the vertices of a given planar triangle; analogously, spherical area coordinates (SACs) describe the positions of points on a sphere concerning the vertices of a given spherical triangle. In particular, the global coordinate system is obtained by decomposing the globe into several identical triangular regions, constructing local coordinates for each region, and then combining them. Once the SACs have been established, the coordinate isolines form a new class of global grid systems. This kind of grid system has some useful properties: the grid cells exhaustively cover the globe without overlapping and have the same shape, and the grid system has a congruent hierarchical structure and simple relationship with traditional coordinates. These beneficial characteristics are suitable for organizing, representing, and analyzing spatial data.},
DOI = {10.3390/app10020655}
}
@article{AKSMAN88,
title = {Reconnections of vortex filaments},
journal = {Fluid Dynamics Research},
volume = {3},
number = {1},
pages = {239-246},
year = {1988},
issn = {0169-5983},
doi = {https://doi.org/10.1016/0169-5983(88)90072-X},
url = {https://www.sciencedirect.com/science/article/pii/016959838890072X},
author = {M.I. Aksman and E.A. Novikov},
abstract = {The process of break-down and reconnection of vortex filaments is considered by the method of three-dimensional vortex singularities (vortons) in various situations, including oblique interaction of a vortex ring with a boundary in shear flow, shedding of a vortex ring from a horseshoe vortex, instability of elliptic vortex ring, Crow instability of two perturbed antiparallel vortex filaments, merging and subsequent splitting of vortex rings. Special attention is paid to the global integrals (vorticity, momentum, angular momentum) and to the inviscid dissipation of energy. The visualization of the effective vortex core, created by the interference of the vorticity fields of vortons, is presented. The comparisons with other methods of simulation of three-dimensional vortex interactions and with the observations have been made.}
}



@article{PLASMA09,
	doi = {10.1088/1742-6596/180/1/012037},
	url = {https://doi.org/10.1088%2F1742-6596%2F180%2F1%2F012037},
	year = 2009,
	month = {jul},
	publisher = {{IOP} Publishing},
	volume = {180},
	pages = {012037},
	author = {Emmanuel Agullo and Jim Demmel and Jack Dongarra and Bilel Hadri and Jakub Kurzak and Julien Langou and Hatem Ltaief and Piotr Luszczek and Stanimire Tomov},
	title = {Numerical linear algebra on emerging architectures: The {PLASMA} and {MAGMA} projects},
	journal = {Journal of Physics: Conference Series}
	}

@article{SCH16,
title = "A generalized Clebsch transformation leading to a first integral of Navier–Stokes equations",
journal = "Physics Letters A",
volume = "380",
number = "40",
pages = "3258 - 3261",
year = "2016",
issn = "0375-9601",
doi = "https://doi.org/10.1016/j.physleta.2016.07.066",
url = "http://www.sciencedirect.com/science/article/pii/S0375960116305205",
author = "M. Scholle and F. Marner",
keywords = "First integrals, Viscous flow, Potentials, Gauge transformations, Clebsch variables, Mathematical foundations"
}




@article{Hopf19,
    author = {Ohkitani, Koji},
    year = {2019},
    month = {12},
    pages = {},
    title = {Study of the Hopf functional equation for turbulence: Duhamel principle and dynamical scaling},
    volume = {101},
    journal = {Physical Review E},
    doi = {10.1103/PhysRevE.101.013104}
}

@misc{QC20,
    title={Quantum Computation of Fluid Dynamics},
    author={Sachin S. Bharadwaj and Katepalli R. Sreenivasan},
    year={2020},
    eprint={2007.09147},
    archivePrefix={arXiv},
    primaryClass={quant-ph}
}
@article{Vol15,
author = {G.~E.~Volovik},
title={Superfluids in rotation: Landau--Lifshitz vortex sheets vs Onsager--Feynman vortices},
year = {2015},
month = {09},
journal ={UFN},
volume ={185},
pages={970-979},
doi = {10.3367/UFNr.0185.201509h.0970}
}

@article{ZH20,
  title = {One-dimensional nexus objects, network of Kibble-Lazarides-Shafi string walls, and their spin dynamic response in polar-distorted $B$-phase of $^{3}\mathrm{He}$},
  author = {Zhang, K.},
  journal = {Phys. Rev. Research},
  volume = {2},
  issue = {4},
  pages = {043356},
  numpages = {23},
  year = {2020},
  month = {Dec},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevResearch.2.043356},
  url = {https://link.aps.org/doi/10.1103/PhysRevResearch.2.043356}
}

@misc{BMM,
author = {Mikhail Bulgakov},
    title  = {The Master and Margarita},
    year={1966},
    chapter={12},
    howpublished={\url{https://www.weblitera.com/book/?id=205&lng=1&ch=12&l=}}
}

@article{KBL15,
	doi = {10.1088/0954-3899/42/9/094002},
	url = {https://doi.org/10.1088%2F0954-3899%2F42%2F9%2F094002},
	year = 2015,
	month = {aug},
	publisher = {{IOP} Publishing},
	volume = {42},
	number = {9},
	pages = {094002},
	author = {T W B Kibble and Tanmay Vachaspati},
	title = {Monopoles on strings},
	journal = {Journal of Physics G: Nuclear and Particle Physics},
	abstract = {In cosmological scenarios based on grand unification, string theory or braneworlds, many kinds of topological or non-topological defects, including monopoles and cosmic strings, are predicted to be formed in the early Universe. Here we review specifically the physics of composite objects involving monopoles tied to strings. There is a wide variety of these, including for example ‘dumbbells’ and ‘necklaces’, depending on how many strings attach to each monopole and on the extent to which the various fluxes are confined to the strings. We also briefly survey the prospects for observing such structures, the existing observational limits, and potential evidence for a cosmological role.}
}

@article{V20,
  title = {String monopoles, string walls, vortex skyrmions, and nexus objects in the polar distorted $B$ phase of $^{3}\mathrm{He}$},
  author = {Volovik, G. E. and Zhang, K.},
  journal = {Phys. Rev. Research},
  volume = {2},
  issue = {2},
  pages = {023263},
  numpages = {11},
  year = {2020},
  month = {Jun},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevResearch.2.023263},
  url = {https://link.aps.org/doi/10.1103/PhysRevResearch.2.023263}
}

@article{Aji_2001,
   title={Fluctuations in Finite Critical and Turbulent Systems},
   volume={86},
   ISSN={1079-7114},
   url={http://dx.doi.org/10.1103/PhysRevLett.86.1007},
   DOI={10.1103/physrevlett.86.1007},
   number={6},
   journal={Physical Review Letters},
   publisher={American Physical Society (APS)},
   author={Aji, Vivek and Greenfeld, Nigel},
   year={2001},
   month={Feb},
   pages={1007–1010}
}

@article{eyink20, 
title={Stochastic Lagrangian dynamics of vorticity. Part 1. General theory for viscous, incompressible fluids}, 
volume={901}, 
DOI={10.1017/jfm.2020.491}, 
journal={Journal of Fluid Mechanics}, 
publisher={Cambridge University Press}, 
author={Eyink, Gregory L. and Gupta, 
Akshat and Zaki, Tamer A.}, 
year={2020}, 
pages={A2}
}
@article{Dorn94,
   title={Two- and three-point functions in Liouville theory},
   volume={429},
   ISSN={0550-3213},
   url={http://dx.doi.org/10.1016/0550-3213(94)00352-1},
   DOI={10.1016/0550-3213(94)00352-1},
   number={2},
   journal={Nuclear Physics B},
   publisher={Elsevier BV},
   author={Dorn, H. and Otto, H.-J.},
   year={1994},
   month={Oct},
   pages={375–388}
}

@article{ZZ96,
   title={Conformal bootstrap in Liouville field theory},
   volume={477},
   ISSN={0550-3213},
   url={http://dx.doi.org/10.1016/0550-3213(96)00351-3},
   DOI={10.1016/0550-3213(96)00351-3},
   number={2},
   journal={Nuclear Physics B},
   publisher={Elsevier BV},
   author={Zamolodchikov, A. and Zamolodchikov, Al.},
   year={1996},
   month={Oct},
   pages={577–605}
}
@Article{Onsager1949,
author={Onsager, L.},
title={Statistical hydrodynamics},
journal={Il Nuovo Cimento (1943-1954)},
year={1949},
month={Mar},
day={01},
volume={6},
number={2},
pages={279-287},
issn={1827-6121},
doi={10.1007/BF02780991},
url={https://doi.org/10.1007/BF02780991}
}

@article{FS30,
author = { V.M.   Falkner   and   S.W.   Skan },
title = {LXXXV. Solutions of the boundary-layer equations},
journal = {The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science},
volume = {12},
number = {80},
pages = {865-896},
year  = {1931},
publisher = {Taylor & Francis},
doi = {10.1080/14786443109461870},

URL = { 
        https://doi.org/10.1080/14786443109461870
    
},
eprint = { 
        https://doi.org/10.1080/14786443109461870
    
}

}

@misc{WFS21,
   author = "Wikipedia",
   title = "{Falkner-Skan Boundary layer} --- {W}ikipedia{,} The Free Encyclopedia",
   year = "2020",
   url = {https://en.wikipedia.org/wiki/Falkner%E2%80%93Skan_boundary_layer},
   note = "[Online; accessed 29-October-2020]"
}
@misc{AAyush,
    author = "{AAyush Anand}",
    title= "{Computing Enstrophy for the Stable Confined Vortex Surface. PHD thesis}",
    month = "January",
    year ="2022",
    journal = {"Department of Physics,
Trinity College Dublin, University of Dublin proceedings",
January 2022}
}

@article{Finne2003,
author = "{A.P. Finne,  T. Araki,  R. Blaauwgeers,  V.B. Eltsov , N.B. Kopnin , M. Krusius,  L. Skrbek,  M. Tsubota and G.E. Volovik}", 
title= "{An intrinsic velocity-independent criterion for superfluid turbulence}", 
journal ={Nature},
volume =424, 
pages = {1022--1025},
year = 2003
}

% Transition to superfluid turbulence driven by an intrinsic parameter, 
% cond-mat/0304586.

@article{Volovik2003,
author = "{G.E.~Volovik}",
title = "{The Universe in a Helium Droplet}",
journal={Clarendon Press,  Oxford},
year = 2003
}

@article{Bevan1997,
author = "{T.D.C. Bevan , A.J. Manninen , J.B. Cook , J.R. Hook , H.E. Hall,  T. Vachaspati and G.E. Volovik}",
title = {Momentum creation by vortices in superfluid $^3$He as a model of primordial baryogenesis},  
journal ={Nature},  
volume ={ 386},  
pages ={689-692},
year =1997}
% the bibitems to be converted to bibtex  below


@book{VollhardtWolfle,
author = "{D.~Vollhardt and P.~Wölfle}", 
title ={The Superfluid Phases of Helium 3},
publisher ={Taylor \& Francis, London}, 
year =1990
}

 
 @article{Volovik1987,
author = {G.E. Volovik}, 
title ={Linear momentum in ferromagnets}, 
journal={J. Phys. C },
volume = 20, 
pages = {L83--L87},
year =1987
}
 
@article{Kuznetsov2018,
author = "{D.S. Agafontsev,  E.A. Kuznetsov and A.A. Mailybaev}",
title ={"Development of high vorticity structures and geometrical properties of the vortex line representation"},
journal = {Phys. Fluids},
volume ={ 30}, 
page ={095104},
year =2018
}

@article{Volovik1986,
author = {G.E. Volovik}, 
title ={"Wess-Zumino action for the orbital dynamics of $^3$He-A"},
journal ={JETP Lett.},
volume ={44}, 
pages ={185--189},
year =1986
}
 
 
@article{Kuznetsov1980,
author= "{E.A.~Kuznetsov and A.V. ~Mikhailov}",
title ={"On the topological meaning of canonical Clebsch variables"},
journal = {"Physics Letters A"},
volume ={  77}, 
pages ={37--38},
year = 1980
}

@article{Blaha1976,
author ={S. Blaha},
title = {Quantization rules for point singularities in superfluid $^3$He and liquid crystals},
journal ={ Phys. Rev. Lett.},
volume ={ 36}, 
page =874,
year =1976}
 
 @article{VolovikMineev1976,
author ="{G.E. Volovik, V.P. Mineev}", 
title = "{ Vortices with free ends in superfluid $^3$He-A}",
journal ={ JETP Lett.},
volume ={ 23},
page ={593},
year =1976
}

@article{Volovik2000,
author ={G.E.~Volovik}, 
title ="{Monopoles and fractional vortices in chiral superconductors}",  
journal ="{Proc. Natl. Acad. Sc. USA}", 
volume ={97}, 
pages ={2431-2436},
year =2000}



@misc{Chefranov2017,
  doi = {10.48550/ARXIV.1711.04124},
  
  url = {https://arxiv.org/abs/1711.04124},
  
  author = {Chefranov, Sergey G. and Mokhov, Igor I. and Chefranov, Alexander G.},
  
  keywords = {Fluid Dynamics (physics.flu-dyn), Superconductivity (cond-mat.supr-con), FOS: Physical sciences, FOS: Physical sciences},
  
  title = {The hydrodynamic singular vortex on the sphere and the Dirac monopole},
  
  publisher = {arXiv},
  
  year = {2017},
  
  copyright = {arXiv.org perpetual, non-exclusive license}
}


@article{MineyevVolovik1978,
author = "{V.P. Mineyev, G.E. Volovik}", 
 title = "{Planar and linear solitons in superfluid $^3$He}",
journal = "{Phys. Rev. B}",
volume ={ 18}, 
pages ={3197--3203},
year =1978
}


@article{Kibble1982,
author ="{T. W. B. ~Kibble, G.~Lazarides, and Q.~Shafi}",
title ="{Walls bounded by strings}",
journal ="{Phys. Rev. D}",
volume ={ 26}, 
pages ={435--439},
year = 1982
}

@article{Kibble1982b,
author ="{T. W. B. ~Kibble, G.~Lazarides, and Q.~Shafi}",
title = "{Strings in $SO(10)$}",
journal = "{Phys. Lett. B}",
volume ={113},
pages = {237--239},
year =1982
}
@article{Makinen2019,
author ="{J.T. M\"akinen, V.V. Dmitriev, J. Nissinen, J. Rysti, G.E. Volovik, A.N. Yudin, K. Zhang, V.B. Eltsov}",
title = "{Half-quantum vortices and walls bounded by strings in the polar-distorted phases of topological superfluid $^3$He}",
journal = "{Nat. Comm.}",
volume ={10},
page = {237},
year =2019
}

@article{VolovikZhang2020,
author ="{G. E. Volovik, K. Zhang}",
title = "{String monopoles, string walls, vortex-skyrmions and nexus objects in polar distorted B-phase of $^3$He}",
journal = "{Physical Review Research}",
volume ={2},
page = {023263},
year =2020
}

@article{Dzyaloshinskii1980,
author ="{I.E. Dzyaloshinskii, and G.E. Volovick}",
title = "{Poisson brackets in  condensed matter physics}",
journal = "{Ann. Phys.}",
volume ={125},
pages = {67--97},
year =1980
}
 
@article{SalomaaVolovik1987,
author ="{M.M. Salomaa,  G.E. Volovik}",
title = "{Quantized vortices in superfluid $^3$He}",
journal = "{Rev. Mod. Phys.}",
volume ={59},
pages = {533--613},
year =1987
}


@inproceedings{HansonRegge,
  title="{Torsion and quantum gravity: Proceedings of the Integrative Conference on Group Theory
and Mathematical Physics}",
  author={A.J. Hanson and T. Regge},
  year={1978},
  publisher="{University of Texas at Austin}"
}

@article{AuriaRegge,
author ="{R. d'Auria and T. Regge}",
title = "{Gravity theories with asymptotically flat instantons}",
journal = "{Nucl. Phys. B}",
volume ={195},
page = {308},
year =1982
}








% \bibitem{VolovikZubkov2014b}
% G.E. Volovik and M.A. Zubkov,
% Emergent Weyl fermions and the origin of $i=\sqrt{-1}$ in quantum mechanics,
% Pis'ma ZhETF {\bf 99},  552--557 (2014);  JETP Lett. {\bf 99},  481--486  (2014),
% arXiv:1404.4084.
