Abstract: From the regular collision time, τcee, due to multiple Coulomb collisions between electrons an effective electron radius is proposed using the kinetic theory in plasma physics and considering we deal with what we will call a Lorentz-like gas. The effective or equivalent electron radius is deduced by corresponding the total cross section with a collision radius that can be related with the length of the electron and depends on the temperature and density a=a(n;T). This is quite unusual, but ultimately it is a measure that describes an effective radius of the electron based on supposing collision of rigid spheres corresponding to the electrons in a Lorentz-like gas with temperature and density. Unlike other electron size proposals where fixed parameters are taken, the electron radius is deduced from a many-particle system. τcee is compared with the electron-electron relaxation time, τee, obtained calculating the cross section for the momentum transfer. Taking into account typical fusion conditions (TOKAMAK), the equivalent electron radius aT as well as the corresponding electron-electron collision and relaxation times are calculated. Assuming that electron describes a diffusion equation based on Stokes law of viscosity, the friction coefficient α is calculated using the relaxation time and the dynamic viscosity η is deduced from the first order approximation of the Chapmann-Enskog theory for hard-sphere electrons.

Abstract: Hydrogen and some of its derivatives (such as e-methanol, e-methane, and e-ammonia) are promising energy carriers that have the potential to replace conventional fuels, thereby eliminating their harmful environmental impacts. An innovative use of hydrogen as a zero-emission fuel is being a source of weakly-ionized plasma through seeding its combustion products with a small amount of an alkali metal vapor (cesium or potassium). This plasma can be used as the working fluid in supersonic open-cycle magnetohydrodynamic (OCMHD) power generators. In such OCMHD generators, direct-current (DC) electricity is generated directly without moving turbogenerators. In the current study, we quantitatively and qualitatively explore the levels of electric conductivity and the resultant volumetric electric output power density in a typical OCMHD supersonic channel, where thermal equilibrium plasma is accelerated at a Mach number of two (Mach 2) while being subject to a strong applied magnetic field (applied magnetic-field flux density) of five teslas (5 T), and with the assumption of an isothermal temperature of 2,300 K (2,026.85 °C). We varied the total pressure of the pre-ionization seeded gas mixture between 1/16 atm and 16 atm. We varied the seed level between 0.0625% and 16% (pre-ionization mole fraction). We varied the seed type between cesium and potassium. We varied the oxidizer type between air (oxygen-nitrogen mixture, 21%-79% by mole) and pure oxygen. Our results suggest that the ideal power density can reach exceptional levels beyond 1,000 MW/m³ (or 1 kW/cm³). The power density can be enhanced using any of the following techniques: (1) lower total pressures, (2) using cesium instead of potassium for seeding, and (3) using air instead of oxygen as an oxidizer (if the temperature is unchanged). A seed level between 1% and 4% (pre-ionization mole fraction) is recommended (much lower or much higher seed levels are harmful to the OCMHD performance). The seed level that maximizes the electric power is not necessarily the same seed level that maximizes the electric conductivity due to additional thermochemical changes caused by the additive seed.

Abstract: Surface inflows toward solar Active Regions (ARs) are horizontal plasma movements that play a significant role in shaping solar magnetic activity and dynamo processes. This review synthesizes current knowledge on these inflows within solar dynamo frameworks—Babcock-Leighton, Flux Transport, and Mean-Field models highlighting their consistent presence across ARs and their dual impact of enhancing flux cancellation while limiting flux dispersal. Acting as a nonlinear feedback mechanism, inflows modulate polar field buildup and axial dipole amplitude, influencing solar cycle strength, with effects more pronounced in strong cycles. Observational advances, such as helioseismic data and high-resolution imaging, alongside 3D simulations, underscore their ties to meridional circulation and cycle amplitude. Yet, uncertainties remain regarding their drivers—magnetic versus thermal—and their full integration into dynamo models, particularly concerning turbulent pumping and deep flows. This study identifies trends, gaps, and future research directions, emphasizing the critical role of surface inflows in linking local AR dynamics to global solar behaviour.

Abstract: Geophysical and astrophysical flows are characterized by rapid rotation. Simulating these flows requires small timesteps to achieve stability and accuracy. Numerical stability can be greatly improved by implicit integration of the terms that are most responsible for destabilizing the numerical scheme. We have implemented an implicit treatment of the Coriolis force in a rotating spherical shell driven by a radial thermal gradient. We have modified the resulting timestepping code to carry out steady-state solving via Newton’s method, which has no time-stepping error. The implicit terms have the effect of preconditioning the linear systems, which can then be rapidly solved by a matrix-free Krylov method. We compute branches of rotating waves with azimuthal wavenumbers ranging from 4 to 12. As the Ekman number (the non-dimensionalized inverse rotation rate) decreases, the flows are increasingly axially independent and localized near the inner cylinder, in keeping with well-known theoretical predictions and previous experimental and numerical results. The advantage of the implicit over the explicit treatment also increases dramatically with decreasing Ek, reducing the cost of computation by as much as a factor of 10 for Ekman numbers of order 10−5. We carry out continuation in both Rayleigh and Ekman number and obtain interesting branches in which the drift velocity remains unchanged between pairs of saddle-node bifurcations.

Abstract: Within the framework of the Cauchy law of motion, we explore an approach to measuring the Weissenberg effect in complex fluids by using the general Weissenberg number GN_We put forth by Huang et al. (2019). First, we analyze and compare the applications of the primary Weissenberg number N_We and the general Weissenberg number GN_We in two typical viscometric flows and in two non-viscometric flows given by Huilgol (1971) and by Huilgol and Triver (1996), respectively, using an incompressible fluid of grade 2 and the incompressible Reiner-Rivlin fluid. Second, we use both N_We and GN_We to carry out detailed analyses of the three normal stress differences N_1, N_2, and N_3 = N_1 +N_2 by employing the experimental results of Gamonpilas et al. (2016), Singh and Nott (2003), Zarraga et al. (2000), Couturier et al. (2011), and Dai et al. (2013). These results indicate that GN_We outdoes N_We in comprehensively characterizing the Weissenberg effect, a.k.a. the normal stress effect or the elastic effect, in complex fluids in both the viscometric and the non-viscometric flows. Third, we show that the kinematical vorticity number V_K(x,t), namely the Truesdell number, plays a vital role in setting up a necessary condition for the measurement of the Weissenberg effect. From a general, theoretical standpoint, we introduce an intrinsic orthonormal basis (e_1,e_2,e_3) in the same sense of Serrin (1959), which coincides with the conventionally used orthonormal basis if the flow is viscometric, to calculate GN_We so as to measure the Weissenberg effect in a laminar flow of complex fluids, provided that in the flow field there exists at least one spatial point x with some neighborhood in which the Truesdell number V_K(x,t) > 0.

Abstract: Particle in Cell (PIC) simulation has been used to validate a conceptual design for a quasi-spherical, net power, hydrogen plus boron-11 fueled, fusion reactor incorporating high temperature superconducting (HTS) magnets. By burning a fully thermalized plasma, our proposed MET6 reactor uses the principles of Magneto-Electrostatic Trap design of Yushmanov (1980) to improve the classic Polywell design, resulting in a predicted power-balance Q ≈ 1.3. Because the input power consumed by the reactor will barely balance the waste bremsstrahlung radiation, future research must focus on reducing the bremsstrahlung losses to reach practical net power levels. A first step to reducing bremsstrahlung, explored in this paper, is to tune the reactor parameters to reduce the trapped electrons energies.

Abstract: An electrostatic problem for stationary equilibrium of a continuously distributed charge is formulated in the form of finding both the electric field as well as the charge distribution. This is distinct from typical corresponding problems dealing with finding either the electric field or the charge distribution given one of them as input data. Maxwell and mass continuity equations representing the conservation of charge and mass, as well as the evolution of the electromagnetic fields are kinematic equations to be complemented by a momentum equation governing the dynamics of motion of the distributed charge. It is shown that while two types of possible stationary equilibria, one trivial (i.e. zero value of charge density and electric field) and the other one non-trivial (i.e. non-zero values of charge density and electric field) are possible, only the non-trivial one can materialize in reality. Oscillations may and do occur around the non-trivial equilibrium, but yield non-realistic results if they occur around the trivial equilibrium. The latter is the major reason for rejecting the trivial equilibrium and adopting the non- trivial one.

Abstract: In the realm of fluid dynamics, turbulence inherently necessitates the interactions between fluid viscosity and velocity gradients. This study delves into the foundation of fluid motion equations, identifying the determination of the fluid's constitutive equation as the sole artificial element in their derivation. The paper posits that in turbulent flows, characterized by intense velocity gradients, the second-order terms associated with the deformation rate in the constitutive equation must be retained, rather than dismissed. This revelation yields an accurate constitutive equation for viscous fluids, enabling the derivation of fluid dynamics equations tailored for turbulent motion, devoid of adjustable parameters, and thus refining the Navier-Stokes equations. As a practical application, we present an extended version of Prandtl's boundary layer equation and provide a numerical solution for the wedge flow boundary layer. Determination formulation of the second-order viscosity coefficient is proposed and discussed.

Abstract: Numerous high-resolution Euler-type methods have been proposed to resolve smooth flow scales accurately and to simultaneously capture the discontinuities. A disadvantage of these methods is the numerical viscosity of the shocks. In the shock, the flow parameters change abruptly at a distance equal to the mean free path of a gas molecule, which is much smaller than the cell size of the computational mesh. Due to the numerical viscosity, Euler-type methods stretch the parameter change in the shock over a few mesh cells. This paper describes a modification of the semi-Lagrangian Godunov-type method without numerical viscosity for shocks, which was proposed by the author in the previously published paper. In the previous article, a linear law for the distribution of flow parameters was employed for a rarefaction wave when modeling the Shu-Osher problem with the aim of reducing parasitic oscillations. Additionally, the nonlinear law derived from the Riemann invariants was used for the remaining test problems. This article proposes an advanced method, namely, a unified formula for the density distribution of rarefaction waves and modification of the scheme for modeling moderately strong shock waves. The obtained results of numerical analysis including the standard shock-tube problem of Sod, the Riemann problem of Lax, the Shu–Osher shock-tube problem and a few author’s test cases are compared with the exact solution, the data of the previous method and the Total Variation Deminishing (TVD) scheme results. This article delineates the further advancement of the numerical scheme of the proposed method, specifically presenting a unified mathematical formulation for an expanded set of test problems.

Abstract: Lie scale invariance is used to reduce the incompressible Navier-Stokes equations to non-linear ordinary equations. This yields a formulation in terms of logarithmic spirals as independent variables. We give the equations when the spirals lie on cones as well as in planes. The theory gives a locus in cylindrical coordinates of singularities as they arise in the reduced Navier-Stokes equations. We give two formal examples aimed at discovering singularities in the flow; another example is related to a Hele-Shaw cell, and finally we explore the flow through propellers comprised of blades made from congruent logarithmic spirals.

Abstract:

This paper presents a revival of FORTRAN 66 code which calculates flow through curved pipes. Results from the code were originally presented in [Greenspan, D. Secondary flow in a curved tube. J. Fluid Mech. 1973, 57, 167-176]. The coupled non-linear system of partial differential equations was solved numerically using a finite difference method. We demonstrate a step-by-step code revival process and compare original (coarse) results to updated (fine) solutions. Both the structure of streamwise (primary) and secondary flows are covered. The purpose of our paper is to make the code available as modern Fortran for the scientific community. The code runs quickly on modern hardware architectures and enables fast understanding of the physical effects included.

Abstract: This study examines the dynamics of two spheres falling independently in a viscous fluid, highlighting conditions under which a lighter sphere can achieve a higher velocity than a heavier one. Through theoretical modeling and simulations, the motion of spheres with varying densities and radii, released simultaneously in a uniform viscous medium, was analyzed. The investigation considers gravitational, buoyant, and drag forces, with the spheres moving under identical initial conditions and without mutual interaction. The results confirm the well-established case where the heavier sphere exhibits a greater terminal velocity. However, an intriguing phenomenon is identified: under specific conditions, a lighter sphere can surpass its counterpart in terminal velocity. Additionally, when spheres of equal weight are compared, the denser sphere consistently attains a higher terminal velocity. The study reveals non-trivial time-dependent acceleration patterns, with alternating dominance between heavier and lighter spheres before terminal velocities are reached. Furthermore, the order of impact with the ground is shown to depend on the release height, illustrating a complex interplay of forces. These findings offer novel insights into fluid dynamics, with implications for education and engineering applications.

Abstract: The early stages of flame dynamics and the development and evolution of tulip flames in closed tubes of various aspect ratios and in a half-open tube are studied by solving the fully compressible reactive Navier–Stokes equations using a high-order numerical method coupled to detailed chemical models in stoichiometric hydrogen/air and methane/air mixtures. The use of adaptive mesh refinement (AMR) provides adequate resolution of the flame reaction zone, pressure waves, and flame-pressure wave interactions. The purpose of this study is to gain a deeper insight into the influence of chemical kinetics on the combustion regimes leading to the formation of a tulip flame and its subsequent evolution. The simulations highlight the effect of laminar flame velocity and reaction order on the physical mechanism of tulip flame formation and evolution. It is shown that the intensity of the pressure and rarefaction waves generated by the flame at the acceleration and deceleration stages depends on the rate of flame acceleration and deceleration. Since the rate of flame acceleration and deceleration depends on the value of the laminar flame velocity, tulip flame formation and evolution are much faster in a highly reactive mixture.

Abstract: In this review paper the equations of motion describing the fluid dynamics of the ionosphere are constructed step by step, so that any master or post-graduate student may get familiar with the general theory of the “traditional” approach to Ionospheric Physics, in which chemicals forming the Earth’s upper atmosphere are represented as fluids in mutual interaction. The hypotheses on which the smooth-field fluid representation is based are discussed in terms of microscopic dynamics of the gas particles: this discussion is oriented to prepare the reader for the post-fluid approaches to the physics of turbulence, to be treated in forthcoming manuscripts. The fluid dynamical picture of the ionosphere is the most classical and conceptually simple one, and this makes it extremely widespread in terms of theoretical models and applications.

Abstract: In the work, within the framework of the self-consistent model of arc discharge, simulations of plasma parameters in an argon/methane mixture were performed taking into account the evaporation of the electrode material in the case of a refractory and non-refractory cathode. It is shown that in the case of a refractory tungsten cathode, almost the same methane conversion rate is observed, which leads to almost the same values ​​of the concentration of the main methane conversion products C, C2, H at different values ​​of the discharge current density. However, with an increase in the current density, the evaporation rate of copper atoms from the anode increases and a jump in the I-V characteristic is observed, caused by a change in the plasma-forming ion. This fact is due to the lower ionization energy of copper atoms compared to argon atoms. In this mode, one should expect an increase in metal-carbon nanoparticles. It is shown that in the case of a non-refractory copper cathode, the discharge characteristics and the component composition of the plasma depend on the field enhancement factor near the cathode surface. It has been demonstrated that increasing the field enhancement factor leads to more efficient thermal field emission, lowering the cathode surface temperature and the gas temperature in the discharge gap. This leads to the fact that in the arc discharge mode with a non-refractory copper cathode, the dominant types of particles from which the nanostructure can begin to be synthesized in descending order are copper atoms Cu, carbon clusters C2 and carbon atoms C.

Abstract: Due to the geostrophic balance, horizontal divergence-free is often assumed when analyzing large-scale oceanic flows. However, the geostrophic balance is a leading-order approximation. We investigate the statistical feature of weak horizontal compressibility in the Gulf of Mexico by analyzing drifter data (the Grand LAgrangian Deployment (GLAD) experiment and the LAgrangian Submesoscale ExpeRiment (LASER)) based on the asymptotic probability density function of the angle between velocity and acceleration difference vectors in a strain-dominant model. The results reveal a notable divergence at scales between 10 km and 300 km, which is stronger in winter (LASER) than in summer (GLAD). We conjecture that the divergence is induced by wind stress with its curl parallel to the earth’s rotation.

Abstract:

The ionized metal physical vapor deposition (IMPVD), which is operated at a very low pressure to take advantage of the metal sputtering effect on the target surface, has unique properties compared with the conventional DC magnetron sputtering. In this study, we investigated the effect of the rotating magnetic field on the plasma formation of the IMPVD to enhance the deposition uniformity. A two-dimensional particle-in-cell Monte Carlo simulation utilizes the exact cross-section data of the Cu ion collisions and calculates the particle trajectories under specific magnetic field profiles. This new methodology gives guidance for the design of the magnetic field profiles of IMPVD and an understanding of the physical mechanism.

Abstract: The minimalist approach in the study of perturbations in fluid dynamics and magnetohydrodynamics consists in describing their evolution in the linear regime using a single first-order ordinary differential equation, dubbed principal equation. The dispersion relation is found from the requirement the solution of the principal equation to be continuous and satisfy certain boundary conditions in each specific problem. The formalism is presented for flows in cartesian geometry and applied to classical cases, such as the magnetosonic and gravity waves, the Rayleigh-Taylor and Kelvin-Helmholtz instabilities. For the latter we discuss the influence of compressibility and the magnetic field, and also derive analytical expressions for the growth rates in the case of two fluids with the same characteristics.

Abstract: Dielectric barrier discharge microplasma has various applications such as flow control, surface treatment, air treatment or biomedical applications. Microplasma was used for the inactivation of Escherichia coli, Staphylococcus aureus and Pseudomonas aeruginosa. Bacterial strains spread on Petri dishes containing Nutrient Agar were treated with microplasma and after incubation, inhibition zones were observed. By comparison, the experiments carried out with the already-grown bacteria on the Petri dish did not show any inhibitory response. Environmental air was used as discharge gas. The reactive oxygen and nitrogen species mainly carry out the inactivation process. A negative pulse voltage energized the microplasma electrodes. The microplasma treatment was the most potent against S. aureus, followed by E. coli, and P. aeruginosa, which was the least susceptible bacteria from the tested strains. An increase in the inhibitory efficiency was observed with the increase of discharge voltage from -1.5 kV to -1.7 kV. This research proved the efficiency of microplasma in biological decontamination and provides valuable insights of the inactivation of bacteria carried out with a technology that is suitable for easy integration and portability.

Abstract: An advection-diffusion solver has been applied to assess how stent strut shape and position impact the development of a pro-thrombotic region within the stented human artery. We use a suitably parameterised advection-diffusion equation with a source term that is spatially uniform within a certain sub-domain of interest, to compute a ``time concentration''. The latter will serve as a surrogate quantity for ``age'' of fluid parcels, i.e., the time the fluid parcel has spent in the sub-domain. This is a particularly useful concept in the context of coronary artery haemodynamics, where blood stasis (or residence time) is recognised as the most important factor in thrombotic initiation. Our novel method has a very straightforward and convenient single lattice Boltzmann simulation framework encapsulation. We compute, present and correlate our residence time surrogate with a range of traditional haemodynamic metrics (wall shear stress, shear rate and re-circulation region shapes) and finally assess how these data can be used to quantify the risk of thrombus formation.