A formula for the turbulent Prandtl number is derived in terms of local variables available from two-equations turbulence models. The derivation is a direct consequence of the expected square additivity of the molecular and turbulent parameters defining the effective viscosity and the effective conductivity. The formula does not degenerate and leads to a Kays like formulation if approximated. Its utility and its limitation are discussed.

This paper presents a novel theoretical and computational methodology for the generation of an onset turbulent field with prescribed properties in the numerical simulation of an arbitrary viscous flow. The methodology is based on the definition of a suitable distribution of volume force terms in the right–hand side of the Navier–Stokes equations. The distribution is represented by harmonic functions that are randomly variable in time and space. The intensity of the distribution is controlled by a simple PID strategy in order to obtain that the generated turbulent flow matches a prescribed turbulence intensity. A further condition is that a homogeneous isotropic flow is es- tablished downstream of the region where volume force terms are imposed. Although it is general, the proposed methodology is primarily intended for the computational modelling of hydrokinetic turbines in turbulent flows representative of tidal or riverine installations. A first numerical applica- tion is presented by considering the injection of homogeneous and isotropic turbulence with 16% intensity into a uniform unbounded flow. The analysis of statistical properties as auto-correlation, power spectral density, probability density functions, demonstrates that the generated flow tends to achieve satisfactory levels of stationarity and isotropy, whereas the simple control strategy used determines overestimated turbulent intensity levels.

Spatiotemporal dynamics of the atmospheric kinetic energy and its components caused by the ordered and turbulent motions of air masses are estimated from minisodar measurements of three velocity vector components and their variances within the lowest 5–200 m layer of the atmosphere, with a particular emphasis on the turbulent kinetic energy. The layered structure of the total atmospheric kinetic energy has been established. From the diurnal hourly dynamics of the altitude profiles of the turbulent kinetic energy (TKE) retrieved from minisodar data, four layers are established by the character of the altitude TKE dependence, namely, the near-ground layer, the surface layer, the layer with a linear TKE increase, and the transitive layer above. In the first layer, the most significant changes of the ТКЕ were observed in the evening hours. In the second layer, no significant changes in the TKE values were observed. A linear increase in the TKE values with altitude was observed in the third layer. In the fourth layer, the TKE slightly increased with altitude and exhibited variations during the entire observation period. The altitudes of the upper boundaries of these layers depended on the time of day. The MKE values were much less than the corresponding TKE values, they did not exceed 50 m²/s². From two to four MKE layers were distinguished based on the character of its altitude dependence. The two-layer structures were observed in the evening and at night (under conditions of the stable atmospheric boundary layer). In the morning and daytime, the four-layer MKE structures with intermediate layers of linear increase and subsequent decrease in the MKE values were observed. Our estimates demonstrated that the ТКЕ contribution to the total atmospheric kinetic energy considerably (by a factor of 2.5–3) exceeded the corresponding МКЕ contribution.

Computational rhinology is a specialized branch of biomechanics leveraging engineering techniques for mathematical modelling and simulation to complement the medical field of rhinology. Computational rhinology has already contributed significantly to advancing our understanding of the nasal function, including airflow patterns, mucosal cooling, particle deposition, and drug delivery, and is foreseen as a crucial element in e.g. the development of virtual surgery as a clinical, patient-specific decision support tool. The current paper delves into the field of computational rhinology from a nasal airflow perspective, highlighting the use of computational fluid dynamics to enhance diagnostics and treatment of breathing disorders. The paper consists of three distinct parts – an introduction to and review of the field of computational rhinology, a review of published literature on in vitro and in silico studies of nasal airflow, and the presentation and analysis of previously unpublished high fidelity CFD simulation data of in silico rhinomanometry. While the two first parts of the paper summarize the current status and challenges in the application of computational tools in rhinology, the last part addresses the gross disagreement commonly observed when comparing in silico and in vivo rhinomanometry results. It is concluded that this discrepancy cannot readily be explained by CFD model deficiencies caused by poor choice of turbulence model, insufficient spatial or temporal resolution, or neglecting transient effects. Hence, alternative explanations such as nasal cavity compliance or drag effects due to nasal hair should be investigated.

This paper brings to fruition recently found \cite{migdal2023exact} exact reduction of decaying turbulence in the Navier-Stokes equation in $3 + 1$ dimensions to a Number Theory problem of finding the statistical limit of the Euler ensemble. We reformulate the Euler ensemble as a Markov chain and show the equivalence of this formulation to the \textbf{quantum} statistical theory of $N$ fermions on a ring, with an external field related to the random fractions of $\pi$. We find the solution of this system in the turbulent limit $N\to \infty, \nu \to 0$ in terms of a complex trajectory (instanton) providing a saddle point to the path integral over the density of these fermions. This results in an analytic formula for the observable correlation function of vorticity in wavevector space. This is a full solution of decaying turbulence from the first principle without approximations or fitted parameters. The energy spectrum decays as $k^{-\frac{7}{2}}$. We compute resulting integrals in \Mathematica{} and present effective index $n(t) = -t\partial_t \log E $ for the energy decay as a function of time Fig.\ref{fig::NPlot}. The asymptotic value of the effective index in energy decay $n(\infty) = \frac{5}{4}$, but the universal function $n(t)$ is neither constant nor linear.

We have found an infinite dimensional manifold of exact solutions of the Navier-Stokes loop equation for the Wilson loop in decaying Turbulence in arbitrary dimension $d >2$. This solution family is equivalent to a fractal curve in complex space $\mathbb C^d$ with random steps parametrized by $N$ Ising variables $\sigma_i=\pm 1$, in addition to a rational number $\frac{p}{q}$ and an integer winding number $r$, related by $\sum \sigma_i = q r$. This equivalence provides a \textbf{dual} theory describing a strong turbulent phase of the Navier-Stokes flow in $\mathbb R_d$ space as a random geometry in a different space, like ADS/CFT correspondence in gauge theory. From a mathematical point of view, this theory implements a stochastic solution of the unforced Navier-Stokes equations. For a theoretical physicist, this is a \textbf{quantum} statistical system with integer-valued parameters, satisfying some number theory constraints. Its long-range interaction leads to critical phenomena when its size $N \rightarrow \infty$ or its chemical potential $\mu \rightarrow 0$. The system with fixed $N$ has different asymptotics at odd and even $N\rightarrow \infty$, but the limit $\mu \rightarrow 0$ is well defined. The energy dissipation rate is analytically calculated as a function of $\mu$ using methods of number theory. It grows as $\nu/\mu^2$ in the continuum limit $\mu \rightarrow 0$, leading to anomalous dissipation at $\mu \propto \sqrt{\nu} \to 0$. The same method is used to compute all the local vorticity distribution, which has no continuum limit but is renormalizable in the sense that infinities can be absorbed into the redefinition of the parameters. The small perturbation of the fixed manifold satisfies the linear equation we solved in a general form. This perturbation decays as $t^{-\lambda}$, where the anomalous dimensions $\lambda$ satisfy the spectral equation \eqref{spectralEq}. The spectrum becomes a continuum in the statistical limit $N \to \infty$, presumably leading to multifractal phenomena.

A rigid protruding surface, agitator and vortex generator often dissipate more energy than to produce a satisfied turbulence production. In contrast, a passively-oscillating flexible protruding surface has the ability in generating greater turbulence level. In the current study, a circular finite cylinder (cantilever) was used as the geometry of the rigid and protruding surface. They were varied through the aspect ratio (AR) and materials. Also, a local Reynolds number within the subcritical flow range (102<ReD<105) was considered. The results from the rigid protruding surface (finite cylinder) is served as a validation to the published results and benchmark to the improve-ment of the turbulence generated by the flexible protruding surface. It was mentioned in the pre-vious work that the increment of turbulence production by the flexible cylinder is speculated to be oscillation, this work investigates the validity of the speculation through manipulating the struc-tural stiffness of the flexible cylinder by employing different materials. The results have further demonstrated that the flexible cylinder is capable of generating a greater turbulence through the examination of turbulence intensity, turbulence production term and Reynolds stress. All the flex-ible cylinders that oscillate show increment in turbulence production but at a different percentage. The cylinders studied in this work ranged from the least structural stiffness (EVA), moderate (al-uminium) to the highest structural stiffness (carbon steel). Through studying the normalized am-plitude responses graph of the flexible cylinder, it is identified that the oscillating motion does in-deed contribute to increment. A further investigation into the results, it is found that the factor which governs the increment is the structural velocity instead of just oscillating motion alone.

Physics-informed neural networks are a promising method to yield surrogate models of flow fields. We present a metamodeling technique for variable geometries based on physics-informed neural networks. The method was applied to the DU99W350 airfoil at a Reynolds number of 1×10⁵. The model predicted the Reynolds-averaged velocity and pressure field around the airfoil for arbitrary angles of attack between 10.0° and 17.5°. The model was trained with data from CFD simulations for a limited set of angles of attack. Additionally, satisfaction of the a priori known boundary conditions as well as the Reynolds-averaged Navier-Stokes equations were trained. A sensitivity analysis concerning the Reynolds number, the amount and distribution of training data, and the turbulence model was conducted showing the superiority of the pseudo-Reynolds stress method and the demand of labeled training data in the domain. The trained network was capable of predicting the developing flow separation on the suction surface and exhibited excellent agreement with CFD results even in the proximity to the wall for interpolations as well as extrapolations from the labeled data set.

In a power plant that uses seawater as a coolant, a debris filter is required to remove foreign substances from the seawater, and differential pressure leads to a decrease in the coolant flow rate, leading to a decrease in power generation efficiency. In this study, analysis was performed under different initial flow velocity conditions of 1.5m/s, 2.0m/s, and 2.5m/s for a debris filter used in a power plant to understand flow characteristics in CTCS. The flow and differential pressure characteristics of a CTCS with an installed debris filter were considered in a comparative analysis of velocity, pressure, and turbulent kinetic energy distribution. The results confirmed that a vortex was generated in the pipe with the debris filter, apparently due to the collision of the flow with the bracket of the debris filter. As the flow rate increased, the range of the vortex increased, causing a loss in flow.

In the present paper, an aerodynamic investigation of a high-speed train is performed. In the first section of this article, a generic high-speed train against a turbulent flow is simulated, numerically. The Reynolds-Averaged Navier-Stokes (RANS) equations combined with the SST turbulence model are applied to solve incompressible turbulent flow around a high-speed train. Flow structure, velocity and pressure contours and streamlines at some typical wind directions are the most important results of this simulation. The maximum and minimum values are specified and discussed. Also, the pressure coefficient for some critical points on the train surface is evaluated. In the following, the wind direction influence the aerodynamic key parameters as drag, lift, and side forces at the mentioned wind directions are analyzed and compared. Moreover, the effects of velocity changes (50, 60, 70, 80 and 90 m/s) are estimated and compared on the above flow and aerodynamic parameters. In the second section of the paper, various data-driven methods including Gene Expression Programming (GEP), Gaussian Process Regression (GPR), and random forest (RF), are applied for predicting output parameters. So, drag, lift and side forces and also minimum and a maximum of pressure coefficients for mentioned wind directions and velocity are predicted and compared using statistical parameters. Obtained results indicated that RF in all coefficients of wind direction and most coefficients of free stream velocity provided the most accurate predictions. As a conclusion, RF may be recommended for the prediction of aerodynamic coefficients.

The fundamental challenge for the structural design of complicated shapes and lightweight structures such as Tensile Membrane Structures (TMS) is a reliable estimation of lateral loading such as wind load. Wind pressure coefficients can’t be correctly calculated by standards for a large range of intricate forms of structures. Computational Fluid Dynamics (CFD), a strong computational technique for evaluating wind pressure distribution on complicated geometry, can be used to determine wind-related parameters. The average wind related-distributions for the tensile membrane surface are validated with a few contributions from prior studies, which are important to validate with benchmarks in experimental wind tunnel experiments. For the double-curved surface, the results show good agreement between experimental tests and CFD simulations. In this study, CFD simulation was used to calculate the mean surface pressure coefficient (Cp) for generic shapes and tensile membrane forms using the steady Reynolds-Averaged Navier-Stokes (RANS) technique. Wind force coefficients and the effect of wind directions are also explored across a wide range of classical and tensile forms. The purpose of the current research is to look at the effect of wind assault angle on the Cp distribution for tensile membrane structures and general shapes.

The nonlocality (superdiffusion) of turbulence is expressed in the empiric Richardson t3 scaling law for the mean square of the mutual separation of a pair of particles in a fluid or gaseous medium. The development of the theory of nonlocality of various processes in physics and other sciences based on the concept of Lévy flights resulted in the idea of Shlesinger and colleagues about the possibility of describing the nonlocality of turbulence using a linear integro-differential equation with a slowly falling kernel. The close approach developed by us made it possible to establish the closeness of the superdiffusion parameter of plasma density fluctuations moving across a strong magnetic field in a tokamak to the Richardson law. In this paper, we show the possibility of a universal description of the characteristics of nonlocality of transfer in a stochastic medium (including turbulence of gases and fluids) using the Biberman-Holstein approach to the transfer of excitation of a medium by photons, generalized to take into account the finiteness of the velocity of excitation carriers. This approach enables us to propose a scaling that generalizes Richardson's t3 scaling law to the combined regime of Lévy flights and Lévy walks.

Based on the insight gained from single jet analysis performed earlier [1], CFD analysis on turbulent jets impinging on one another at an angle was performed. Multiple impingement angles were considered for this study to gain better understanding of the parameters affecting resultant jet growth and velocity distribution. From the study of single jet, it was concluded that the SST k-ω turbulence model was the ideal turbulence model capable of accurately predicting the flow physics of the jets exiting a fully developed pipe at low Reynolds number. Hence, for the study of impinging jets, SST k-ω turbulence model was used to study the velocity and jet growth characteristics. It became evident that the mesh alignment with the velocity vector at exit of the pipe domain plays a crucial role in the accuracy of the results. The parameter used to evaluate this condition was identified as False Diffusion and was observed to affect the TKE parameter significantly. Methods to reduce false diffusion are also discussed in this article. Based on the mesh obtained from the grid sensitivity study, jets impinging at 30, 45 and 60 degrees at Reynolds number of 7500 were numerically analyzed. It was observed that the profile of the resultant jet closely matched with the prediction of elliptical profile predicted by past researchers, [2] and [3]. Also, it was seen that higher jet growth was predicted in case of jets impinging at a higher impingement angle.

Tidal stream energy is a low carbon energy source. Tidal stream turbines operate in a turbulent environment, and the effect of the structure between the turbine and seabed on this environment is not fully understood. An experimental study using 1:72 scale models based on a commercial turbine design was carried out to study the support structure influence on turbulence intensity around turbine blades. The study was conducted using the wave-current tank at LABIMA, University of Florence. A realistic flow environment (ambient turbulent intensity = 11%) was established. Turbulence intensity was measured upstream and downstream of a turbine mounted on two different support structures (one resembling a commercial design, the other the same with an additional vertical element), in order to quantify any variation in turbulence and performance between the support structures. Turbine drive power was used to calculate power generation. Acoustic Doppler Velocimetry was used to record and calculate upstream and downstream turbulence intensity. In otherwise identical conditions, performance variation of only 4% was observed between two support structures. Turbulent intensity at 1, 3 and 5 blade diameters, both upstream and downstream, showed variation up to 21% between the two cases. The additional turbulent structures generated by the additional element of the second support structure appears to cause this effect, and the upstream propagation of turbulent intensity is believed to be permitted by surface waves. This result is significant for the prediction of turbine array performance.

Non-normal mode stability analysis has long been employed to study linear transient characteristics of wall bounded shear flows. However, the application of this approach to investigate shear flows with stratified thermal conditions (STCF) has received limited attention. This paper examines thermal effects on Taylor-Couette flow. The results in this study indicate the possibility of a subcritical bifurcation in stratified Taylor-Couette flow.

The three-dimensional single fin configuration finds application in an intake geometry where the cowl-shock wave interacts with the side-wall boundary-layer. Accurate numerical simulation of such three-dimensional shock/turbulent boundary-layer interaction flows, which are characterized by the appearance of strong crossflow separation, is a challenging task. Reynolds-averaged Navier-Stokes computations using the shock-unsteadiness modified Spalart-Allmaras model is carried out at Mach of 5 at large fin angle of 23^◦. The computed results using the modified model are compared to the standard Spalart-Allmaras model and validated against the experimental data. The focus of work is to implement the modified model and to study the flow physics in detail in the complex region of swept-shock-wave turbulent boundary-layer interaction in terms of the shock structure, expansion fan, shear layer and the surface streamlines. The flow structure is correlated to the wall pressure and skin friction in detail. It is observed that the standard model predicts an initial pressure location downstream of the experiments. The modified model reduces the eddy viscosity at the shock and predicts close to the experiments. Overall, the surface pressure using modified model is predicted accurately at all the locations. The skin friction is under predicted by both the models in the reattachment region and is attributed to the poor performance of turbulence models due to flow laminarization.

This review is a first attempt at bringing together various concepts from research on wall- and magnetically-bounded turbulent flows. Brief reviews of both fields are provided: The main similarities identified are coherent (turbulent) structures, flow generation and transport barriers. Examples are provided and discussed.

Unsupervised physics-informed deep learning can be used to solve computational physics problems by training neural networks to satisfy the underlying equations and boundary conditions without labeled data. Parameters such as network architecture and training method determine the training success. However, the best choice is unknown a priori as it is case specific. Here, we investigated network shapes, sizes, and types for unsupervised physics-informed deep learning of the two-dimensional Reynolds-averaged flow around cylinders. We trained mixed-variable networks and compared them to traditional models. Several network architectures with different shape factors and sizes were evaluated. The models were trained to solve the Reynolds-averaged Navier-Stokes equations incorporating Prandtl's mixing length turbulence model. No training data were deployed to train the models. The superiority of the mixed-variable approach was confirmed for the investigated high Reynolds number flow. The mixed-variable models were sensitive to the network shape. For the two cylinders, differently deep networks showed superior performance. The best fitting models were able to capture important flow phenomena such as stagnation regions, boundary layers, flow separation, and recirculation. We also encountered difficulties when predicting high Reynolds number flows without training data

In line with Pomeau’s conjecture about the relevance of directed percolation (DP) to turbulence onset/decay in wall-bounded flows, we propose a minimal stochastic model dedicated to the interpretation of the spatially intermittent regimes observed in channel flow before its return to laminar flow. Numerical simulations show that a regime with bands obliquely drifting in two stream-wise symmetrical directions bifurcates into an asymmetrical regime, before ultimately decaying to laminar flow. The model is expressed in terms of a probabilistic cellular automaton evolving von Neumann neighbourhoods with probabilities educed from a close examination of simulation results. It implements band propagation and the two main local processes: longitudinal splitting involving bands with the same orientation, and transversal splitting giving birth to a daughter band with orientation opposite to that of its mother. The ultimate decay stage observed to display one-dimensional DP properties in a two-dimensional geometry is interpreted as resulting from the irrelevance of lateral spreading in the single-orientation regime. The model also reproduces the bifurcation restoring the symmetry upon variation of the probability attached to transversal splitting, which opens the way to a study of the critical properties of that bifurcation, in analogy with thermodynamic phase transitions.

RANS simulations have been broadly used to investigate turbulence in the oceans and atmosphere. Within these environments there are a multitude of tracers undergoing reactions (eg. phytoplankton growth, chemical reactions). The distribution of these reactive tracers is strongly influenced by turbulent mixing. With a 50 member ensemble of two dimensional Rayleigh-Taylor induced turbulent mixing, we show that the dynamics of a reactive tracer growing according to Fisher’s equation are poorly captured by the mean. A fluctuation-dependent sink introduced by Reynolds averaging Fisher’s equation transfers concentration from the mean to the fluctuations. We compare the dynamics of the reactive tracer with those of a passive tracer. The reaction causes the concentration of reactive tracer to increase thereby increasing Fickian diffusion and allowing the reactive tracer to diffuse into turbulent structures that the passive tracer cannot reach. A positive feedback between turbulent mixing and fluctuation growth is identified. We show that eddy viscosity and diffusivity parameterizations fail to capture the bulk trends of the system and identify a need for negative eddy diffusivities. One must therefore be cautious when interpreting RANS results for reactive tracers.

The DNS of film boiling requires strong computational resources that are difficult to obtain for a daily CFD use by the practitioners of the industrial R&amp;D experts. On the other hand, the film boiling experiments are associated with the usage of the expensive and highly sophisticated apparatus, and the research to this end is found to be relatively difficult due to high heat flow rates that are present in the process itself. When combined with a transient heat conduction in a solid, the problem becomes significantly difficult. Therefore, a novel method in computation of conjugate heat transfer during film boiling in a quiescent liquid has been proposed in this paper. The method relies on the solution of mass, momentum and energy conservation equations in a two-fluid framework, supplemented with the appropriate closures. Furthermore, the turbulent flow has been found as an important parameter in obtaining the accurate solution of the temperature field evolution in a solid specimen, via the proper modeling of turbulent kinetic energy (TKE) value, that has been imposed as a constant value, i.e., the frozen turbulence approach. It was found, in addition, that the appropriate TKE value can be obtained by use of Kelvin-Helmholtz instability theory in conjunction with the boundary layer theory. The obtained results show excellent agreement with the experimental data within the first 15 s of the experiment, i.e., the first ca. 10 % of the total duration of the film boiling mode of heat transfer. Furthermore, the heat transfer coefficient has matched the error bands prescribed by the authors of the paper that has presented the correlations, whilst the averaged values are far beyond this band, i.e., are slightly more than 30 % higher. The further inspection has revealed a measure of similarity between the computational result of the volume fraction field distribution and the experiment, thus confirming the capability of the method to obtain realistic interface evolution in time. The method has shown full capability for further pursuing the industrial-scale film boiling problems that involve turbulent flow and the conjugate heat transfer approach.

In this paper, spatial pulse position modulation (SPPM) is used as a case study to investigate the performance of the optical spatial modulation (SM) technique in outdoor atmospheric turbulence (AT). A closed-form expression for the upper bound on the asymptotic symbol error rate (SER) of SPPM in AT is derived and validated by closely-matching simulation results. The error performance is evaluated in weak to strong AT conditions. As the AT strength increases from the weak to strong, the channel fading coefficients become more dispersed and differentiable. Thus, a better error performance is observed under moderate-to-strong AT compared to weak AT. The performance in weak AT can be improved by applying unequal power allocation to make FSO links more distinguishable at the receiver. Receive diversity is considered to mitigate irradiance fluctuation and improve the robustness of the system to turbulence-induced channel fading. The diversity order is computed as half of the number of detectors. Performance comparisons, in terms of energy and spectral efficiencies, are drawn between the SPPM scheme and conventional MIMO schemes such as repetition coding and spatial multiplexing.

A practical wind farm controller for production maximisation based on coordinated control is presented. The farm controller emphasises computational efficiency without compromising accuracy. The controller combines Particle Swarm Optimisation (PSO) with a turbulence intensity based Jensen wake model (TI-JM) for exploiting the benefits of either curtailing upstream turbines using coefficient of power ($C_P$) or deflecting wakes by applying yaw-offsets for maximising net farm production. First, TI-JM is evaluated using convention control benchmarking WindPRO and real time SCADA data from three operating wind farms. Then the optimized strategies are evaluated using simulations based on TI-JM and PSO. The innovative control strategies can optimise a medium size wind farm, Lillgrund consisting of 48 wind turbines, requiring less than 50 seconds for a single simulation, increasing farm efficiency up to a maximum of 6% in full wake conditions.