Recent zbMATH articles in MSC 76Fhttps://www.zbmath.org/atom/cc/76F2021-11-25T18:46:10.358925ZWerkzeugGlobal regularity for solutions of the Navier-Stokes equation sufficiently close to being eigenfunctions of the Laplacianhttps://www.zbmath.org/1472.352712021-11-25T18:46:10.358925Z"Miller, Evan"https://www.zbmath.org/authors/?q=ai:miller.evanSummary: In this paper, we will prove a new, scale critical regularity criterion for solutions of the Navier-Stokes equation that are sufficiently close to being eigenfunctions of the Laplacian. This estimate improves previous regularity criteria requiring control on the \(\dot{H}^\alpha\) norm of \(u,\) with \(2\leq \alpha <\frac{5}{2}\), to a regularity criterion requiring control on the \(\dot{H}^\alpha\) norm multiplied by the deficit in the interpolation inequality for the embedding of \(\dot{H}^{\alpha -2}\cap\dot{H}^{\alpha}\hookrightarrow \dot{H}^{\alpha -1}\). This regularity criterion suggests, at least heuristically, the possibility of some relationship between potential blowup solutions of the Navier-Stokes equation and the Kolmogorov-Obhukov spectrum in the theory of turbulence.Enhanced diffusivity in perturbed senile reinforced random walk modelshttps://www.zbmath.org/1472.352912021-11-25T18:46:10.358925Z"Dinh, Thu"https://www.zbmath.org/authors/?q=ai:dinh.thu"Xin, Jack"https://www.zbmath.org/authors/?q=ai:xin.jack-xSummary: We consider diffusivity of random walks with transition probabilities depending on the number of consecutive traversals of the last traversed edge, the so called senile reinforced random walk (SeRW). In one dimension, the walk is known to be sub-diffusive with identity reinforcement function. We perturb the model by introducing a small probability \(\delta\) of escaping the last traversed edge at each step. The perturbed SeRW model is diffusive for any \(\delta>0\), with enhanced diffusivity \((\gg O(\delta^2))\) in the small \(\delta\) regime. We further study stochastically perturbed SeRW models by having the last edge escape probability of the form \(\delta\xi_n\) with \(\xi_n\)'s being independent random variables. Enhanced diffusivity in such models are logarithmically close to the so called residual diffusivity (positive in the zero \(\delta\) limit), with diffusivity between \(O(\frac{1}{|\log\delta|})\) and \(O(\frac{1}{\log |\log\delta|})\). Finally, we generalize our results to higher dimensions where the unperturbed model is already diffusive. The enhanced diffusivity can be as much as \(O(\log^{-2}\delta)\).Boundary control for optimal mixing via Navier-Stokes flowshttps://www.zbmath.org/1472.490052021-11-25T18:46:10.358925Z"Hu, Weiwei"https://www.zbmath.org/authors/?q=ai:hu.weiwei"Wu, Jiahong"https://www.zbmath.org/authors/?q=ai:wu.jiahongAmbit stochasticshttps://www.zbmath.org/1472.600022021-11-25T18:46:10.358925Z"Barndorff-Nielsen, Ole E."https://www.zbmath.org/authors/?q=ai:barndorff-nielsen.ole-eiler"Benth, Fred Espen"https://www.zbmath.org/authors/?q=ai:benth.fred-espen"Veraart, Almut E. D."https://www.zbmath.org/authors/?q=ai:veraart.almut-e-dThis is a monograph on stochastic modelling of complex phenomena which are random and evolve in both time and space. The word `ambit' used as a part of the title appears for the first time in the literature. Available are only a few `ambit' papers and one weekly `Ambit magazine'. Relying on advanced probability the authors define and intensively use the notions `ambit sets' and `ambit fields'. Important applied problems lead to the necessity to develop a systematic and adequate theory. In order to build up good mathematical models, one needs a general theory of non-semimartingale stochastic integration with respect to Volterra processes followed by a detailed analytical study. The author pays a great attention to diverse methods of numerical integration and simulation algorithms. All these are successfully used to suggest and analyze stochastic models in complex areas such as turbulence and stochastic volatility.
The reader will get a good sense of the contents of the book by looking at the chapter names and, in brackets, the names of two randomly chosen sections. Part I. The purely temporally case: 1. Volatility modulated Volterra processes (Lévy processes, semimartingale and non-semimartingale settings). 2. Simulation (a stepwise simulation scheme based on the Laplace representation, simulation based on numerically solving stochastic PDEs). 3. Asymptotic theory for power variation of LSS processes (convergence concept, Asymptotic theory in the non-semimartingale setting). 4. Integration with respect to volatility modulated Volterra processes (integration with respect to VMBV processes, discussion of stochastic integration based on an infinite dimensional approach). Part II. The spatio-temporal case: 5. The ambit framework (integration concepts with respect to a Lévy basis, general aspects of the theory of ambit fields and processes). 6. Representation and simulation of ambit fields (Fourier transformation of ambit fields, representations of ambit fields in Hilbert space). 7. Stochastic integration with ambit fields as integrators (definition of the stochastic integral, relationships to semimartingale integration). 8. Trawl processes (choices for the marginal distribution, inference for trawl processes). Part III. Applications: 9. Turbulence modelling (exponentiated ambit fields and correlators, some remarks on dynamic intermittency). 10. Stochastic modelling on energy spot prices by LSS processes (case study: electricity spot prices from the European energy exchange market, pricing electricity derivatives). 11. Forward curve modelling by ambit fields (properties of the ambit model, application to spread options). Two appendices: A. Bessel functions. B. Generalized hyperbolic distribution. A comprehensive list of References and Index.
The authors have written a fundamental book on contemporary probability theory and its applications. The book can be strongly recommended to theorists and applied scientists.Large-scale structures in stratified turbulent Couette flow and optimal disturbanceshttps://www.zbmath.org/1472.760412021-11-25T18:46:10.358925Z"Zasko, Grigory V."https://www.zbmath.org/authors/?q=ai:zasko.grigory-v"Glazunov, Andrey V."https://www.zbmath.org/authors/?q=ai:glazunov.andrey-v"Mortikov, Evgeny V."https://www.zbmath.org/authors/?q=ai:mortikov.evgeny-v"Nechepurenko, Yuri M."https://www.zbmath.org/authors/?q=ai:nechepurenko.yuri-mSummary: Direct numerical simulation data of a stratified turbulent Couette flow contains two types of organized structures: rolls arising at neutral and close to neutral stratifications, and layered structures which manifest themselves as static stability increases. It is shown that both types of structures have spatial scales and forms that coincide with the scales and forms of the optimal disturbances of the simplified linear model of the Couette flow with the same Richardson numbers.Stochastic modelling in fluid dynamics: Itô versus Stratonovichhttps://www.zbmath.org/1472.760452021-11-25T18:46:10.358925Z"Holm, Darryl D."https://www.zbmath.org/authors/?q=ai:holm.darryl-dSummary: Suppose the observations of Lagrangian trajectories for fluid flow in some physical situation can be modelled sufficiently accurately by a spatially correlated Itô stochastic process (with zero mean) obtained from data which is taken in fixed Eulerian space. Suppose we also want to apply Hamilton's principle to derive the stochastic fluid equations for this situation. Now, the variational calculus for applying Hamilton's principle requires the Stratonovich process, so we must transform from Itô noise in the \textit{data frame} to the equivalent Stratonovich noise. However, the transformation from the Itô process in the data frame to the corresponding Stratonovich process shifts the drift velocity of the transformed Lagrangian fluid trajectory out of the data frame into a non-inertial frame obtained from the Itô correction. The issue is, `Will non-inertial forces arising from this transformation of reference frames make a difference in the interpretation of the solution behaviour of the resulting stochastic equations?' This issue will be resolved by elementary considerations.Fluctuation theorem and extended thermodynamics of turbulencehttps://www.zbmath.org/1472.760462021-11-25T18:46:10.358925Z"Porporato, Amilcare"https://www.zbmath.org/authors/?q=ai:porporato.amilcare"Hooshyar, Milad"https://www.zbmath.org/authors/?q=ai:hooshyar.milad"Bragg, Andrew D."https://www.zbmath.org/authors/?q=ai:bragg.andrew-d"Katul, Gabriel"https://www.zbmath.org/authors/?q=ai:katul.gabriel-gSummary: Turbulent flows are out-of-equilibrium because the energy supply at large scales and its dissipation by viscosity at small scales create a net transfer of energy among all scales. This energy cascade is modelled by approximating the spectral energy balance with a nonlinear Fokker-Planck equation consistent with accepted phenomenological theories of turbulence. The steady-state contributions of the drift and diffusion in the corresponding Langevin equation, combined with the killing term associated with the dissipation, induce a stochastic energy transfer across wavenumbers. The fluctuation theorem is shown to describe the scale-wise statistics of forward and backward energy transfer and their connection to irreversibility and entropy production. The ensuing turbulence entropy is used to formulate an extended turbulence thermodynamics.Modeling the third-order velocity structure function in the scaling range at finite Reynolds numbershttps://www.zbmath.org/1472.760472021-11-25T18:46:10.358925Z"Djenidi, L."https://www.zbmath.org/authors/?q=ai:djenidi.lyazid"Antonia, R. A."https://www.zbmath.org/authors/?q=ai:antonia.robert-anthonySummary: A model for the third-order velocity structure function, \(S_3\), is proposed for closing the transport equation of the second-order velocity structure function, \(S_2\), in the scaling range of finite Reynolds number homogeneous and isotropic turbulence (HIT). The model is based on a gradient type hypothesis with an eddy-viscosity formulation. The present model differs from previous ones in that no assumptions are made with regard to the behaviors of \(S_2\) and \(S_3\) in the scaling range. This allows \(S_3\) to be modeled whether the intermittency of the energy dissipation \(\epsilon\) (as modeled by the intermittency phenomenology) is considered or not. In both cases, the model predicts the same (infinite Reynolds number) asymptotic behavior for \(S_2\). This corresponds to the K41 prediction, i.e., \(S_2 \sim r^{2/3}\). The model yields good agreement against direct numerical simulation data for forced HIT at all scales of motion except in the transition region between the dissipative and scaling ranges. The introduction of a simple bridging function in the model improves significantly the agreement in this region. Furthermore, the model illustrates the effect of the finite Reynolds number on the scaling range and shows that this effect is responsible for the deviation from a power-law behavior.
{\copyright 2021 American Institute of Physics}Extreme dissipation and intermittency in turbulence at very high Reynolds numbershttps://www.zbmath.org/1472.760482021-11-25T18:46:10.358925Z"Elsinga, Gerrit E."https://www.zbmath.org/authors/?q=ai:elsinga.gerrit-e"Ishihara, Takashi"https://www.zbmath.org/authors/?q=ai:ishihara.takashi"Hunt, Julian C. R."https://www.zbmath.org/authors/?q=ai:hunt.julian-c-rSummary: Extreme dissipation events in turbulent flows are rare, but they can be orders of magnitude stronger than the mean dissipation rate. Despite its importance in many small-scale physical processes, there is presently no accurate theory or model for predicting the extrema as a function of the Reynolds number. Here, we introduce a new model for the dissipation probability density function (PDF) based on the concept of significant shear layers, which are thin regions of elevated local mean dissipation. At very high Reynolds numbers, these significant shear layers develop layered substructures. The flow domain is divided into the different layer regions and a background region, each with their own PDF of dissipation. The volume-weighted regional PDFs are combined to obtain the overall PDF, which is subsequently used to determine the dissipation variance and maximum. The model yields Reynolds number scalings for the dissipation maximum and variance, which are in agreement with the available data. Moreover, the power law scaling exponent is found to increase gradually with the Reynolds numbers, which is also consistent with the data. The increasing exponent is shown to have profound implications for turbulence at atmospheric and astrophysical Reynolds numbers. The present results strongly suggest that intermittent significant shear layer structures are key to understanding and quantifying the dissipation extremes, and, more generally, extreme velocity gradients.On features of penetration of vertical free turbulent jets into surface of liquid in narrow channels of different lengthshttps://www.zbmath.org/1472.760492021-11-25T18:46:10.358925Z"Karlikov, V. P."https://www.zbmath.org/authors/?q=ai:karlikov.v-p.1"Nechaev, A. T."https://www.zbmath.org/authors/?q=ai:nechaev.a-t"Tolokonnikov, S. L."https://www.zbmath.org/authors/?q=ai:tolokonnikov.sergei-lvovichSummary: The article presents new experimental results on the penetration of vertical plane and circular turbulent jets through a free surface of a liquid in relatively narrow channels of different extent with a overflow weir runoff mode. The behavior of the obtained experimental correlations for the period of arising self-oscillating flow modes is discussed. The analysis of a number of discovered features of the considered flows is carried out.Numerical simulations of turbulent thermal convection with a free-slip upper boundaryhttps://www.zbmath.org/1472.760502021-11-25T18:46:10.358925Z"Hay, W. A."https://www.zbmath.org/authors/?q=ai:hay.william-a"Papalexandris, M. V."https://www.zbmath.org/authors/?q=ai:papalexandris.miltiadis-vSummary: In this paper, we report on direct numerical and large-eddy simulations of turbulent thermal convection without invoking the Oberbeck-Boussinesq approximation. The working medium is liquid water and we employ a free-slip upper boundary condition. This flow is a simplified model of thermal convection of water in a cavity heated from below with heat loss at its free surface. Analysis of the flow statistics suggests similarities in spatial structures to classical turbulent Rayleigh-Bénard convection but with turbulent fluctuations near the free-slip boundary. One important observation is the asymmetry in the thermal boundary layer heights at the lower and upper boundaries. Similarly, the budget of the turbulent kinetic energy shows different behaviour at the free-slip and at the lower wall. Interestingly, the work of the mean pressure is dominant due to the hydrostatic component of the mean-pressure gradient but also depends on the density fluctuations which are small but, critically, non-zero. As expected the boundary-layer heights decrease with the Rayleigh number, due to increased turbulence intensity. However, independent of the Rayleigh number, the height of the thermal boundary layer at the upper boundary is always smaller than that on the lower wall.Comparison between compressible, dilatable and incompressible fluid hypotheses efficiency in liquid conditions at high pressure and large temperature differenceshttps://www.zbmath.org/1472.760512021-11-25T18:46:10.358925Z"Rodio, Maria Giovanna"https://www.zbmath.org/authors/?q=ai:rodio.maria-giovanna"Bieder, Ulrich"https://www.zbmath.org/authors/?q=ai:bieder.ulrichSummary: This work is devoted to comparing the compressible, dilatable and incompressible modeling approach for reproducing the unsteady TOPFLOW test case PTS TSW 3-4. For this comparison, we use two codes: NEPTUNE\_CFD and TRIO. In one hand, NEPTUNE\_CFD allows adopting the compressible hypothesis with a URANS turbulence approach. On the other hand, TRIO can reproduce the other two assumptions with a LES turbulence approach. At first, the computations have been validated by comparing the numerical results with the experimental data concerning temperature evolution in time. The comparison shows that the incompressible hypothesis presents a more critical error than the other ones. Then, the velocity profiles obtained by the two codes are shown and compared with a twofold objective: first of all, showing a comparison between two turbulence modeling approaches and then to observe the turbulence structure and fluid dynamic developments. The velocity comparison shows an excellent agreement between the two codes.2D turbulence closures for the barotropic jet instability simulationhttps://www.zbmath.org/1472.760522021-11-25T18:46:10.358925Z"Perezhogin, Pavel A."https://www.zbmath.org/authors/?q=ai:perezhogin.pavel-aleksandrovichSummary: In the present work the possibility of turbulence closure applying to improve barotropic jet instability simulation at coarse grid resolutions is considered. This problem is analogous to situations occurring in eddy-permitting ocean models when Rossby radius of deformation is partly resolved on a computational grid. We show that the instability is slowed down at coarse resolutions. As follows from the spectral analysis of linearized equations, the slowdown is caused by the small-scale normal modes damping arising due to numerical approximation errors and nonzero eddy viscosity. In order to accelerate instability growth, stochastic and deterministic kinetic energy backscatter (KEBs) parameterizations and scale-similarity model were applied. Their utilization led to increase of the growth rates of normal modes and thus improve characteristic time and spatial structure of the instability.On URANS congruity with time averaging: analytical laws suggest improved modelshttps://www.zbmath.org/1472.760532021-11-25T18:46:10.358925Z"Layton, W."https://www.zbmath.org/authors/?q=ai:layton.william-j"McLaughlin, M."https://www.zbmath.org/authors/?q=ai:mclaughlin.michaelSummary: The standard 1-equation model of turbulence was first derived by Prandtl and has evolved to be a common method for practical flow simulations. Five fundamental laws that any URANS model should satisfy are
\begin{itemize}
\item[1.] Time window: \(\tau \downarrow 0\) implies \(v_{\text{URANS}}\rightarrow u_{\text{NSE}} \& \tau \uparrow\) implies \(\nu_T\uparrow\)
\item[2.] \(l(x)=0\) at walls: \(l(x)\rightarrow 0\) as \(x\rightarrow walls\),
\item[3.] Bounded energy: \(\sup_t\int \frac{1}{2}|v(x,t)|^2+k(x,t)dx<\infty\)
\item[4.] Statistical equilibrium: \(\lim \sup_{T\rightarrow \infty }\frac{1}{T}\int_0^T\varepsilon_{\text{model}}(t)dt=\mathcal{O}\left( \frac{U^3}{L}\right)\)
\item[5.] Backscatter possible: (without negative viscosities)
\end{itemize}
This report proves that a kinematic specification of the model's turbulence lengthscale by
\[
l(x,t)=\sqrt{2}k^{1/2}(x,t)\tau,
\]
where \(\tau\) is the time filter window, results in a 1-equation model satisfying Conditions 1, 2, 3, 4 without model tweaks, adjustments or wall damping multipliers.
For the entire collection see [Zbl 1467.34001].Reynolds stress anisotropy in flow over two-dimensional rigid duneshttps://www.zbmath.org/1472.760542021-11-25T18:46:10.358925Z"Dey, Subhasish"https://www.zbmath.org/authors/?q=ai:dey.subhasish"Paul, Prianka"https://www.zbmath.org/authors/?q=ai:paul.prianka"Ali, Sk Zeeshan"https://www.zbmath.org/authors/?q=ai:ali.sk-zeeshan"Padhi, Ellora"https://www.zbmath.org/authors/?q=ai:padhi.elloraSummary: Characteristics of turbulence anisotropy in flow over two-dimensional rigid dunes are analysed. The Reynolds stress anisotropy is envisaged from the perspective of the stress ellipsoid shape. The spatial evolutions of the anisotropic invariant map (AIM), anisotropic invariant function, eigenvalues of the scaled Reynolds stress tensor and eccentricities of the stress ellipsoid are investigated at various streamwise distances along the vertical. The data plots reveal that the oblate spheroid axisymmetric turbulence appears near the top of the crest, whereas the prolate spheroid axisymmetric turbulence dominates near the free surface. At the dune trough, the axisymmetric contraction to the oblate spheroid diminishes, as the vertical distance below the crest increases. At the reattachment point and one-third of the stoss-side, the oblate spheroid axisymmetric turbulence formed below the crest appears to be more contracted, as the vertical distance increases. The AIMs suggest that the turbulence anisotropy up to edge of the boundary layer follows a looping pattern. As the streamwise distance increases, the turbulence anisotropy at the edge of the boundary layer approaches the plane-strain limit up to two-thirds of the stoss-side, intersecting the plane-strain limit at the top of the crest and thereafter moving towards the oblate spheroid axisymmetric turbulence.A pressure decomposition framework for aeroacoustic analysis of turbulent jetshttps://www.zbmath.org/1472.760812021-11-25T18:46:10.358925Z"Unnikrishnan, S."https://www.zbmath.org/authors/?q=ai:unnikrishnan.sanil"Gaitonde, Datta V."https://www.zbmath.org/authors/?q=ai:gaitonde.datta-vSummary: Aeroacoustic analyses of jet flows have benefited greatly from a decomposition of turbulent pressure fluctuations into hydrodynamic and acoustic components. This is typically accomplished using signal processing techniques based on phase speeds, coherence properties or spectral analyses. We present an approach, building on the Momentum Potential Theory (MPT) approach of \textit{P. E. Doak} [``Momentum potential theory of energy flux carried by momentum fluctuations'', J. Sound Vib. 131, No. 1, 67--90 (1989; \url{doi:10.1016/0022-460X(89)90824-9})], to split pressure fluctuations into their hydrodynamic, acoustic and entropic, collectively designated fluid-thermodynamic (FT), components. Key advantages are that the approach is applicable everywhere in the jet \textit{i.e}, not restricted to the near-acoustic field, and does not need user-defined thresholds. The effectiveness of the technique is demonstrated by analyzing the flowfields of three simulated jets, to encompass moderate-compressible to supersonic conditions. The statistical properties and wavepacket dynamics of each pressure component, and their relationships with the unsplit pressure are elaborated. The acoustic pressure field has the form of a wavepacket that attenuates downstream and whose modal analysis reveals low-rank behavior. At each Mach number examined, the acoustic pressure also identifies the relative prominence of each of three components: i) waves with upstream propagating energy content (negative group velocity), ii) supersonically traveling radiating downstream waves, and iii) subsonically convected evanescent waves, which follow the convection pattern of hydrodynamic eddies in the turbulent region. With increasing Mach number, the radiating and convected bands of energy move closer to each other. The hydrodynamic pressure also displays a wavepacket structure, but its features are different: it displays large-scale subsonically convected structures even past the core collapse region. Thus, in the turbulent region of the jet, the acoustic pressure displays smaller integral time scales of fluctuations than the hydrodynamic component. The acoustic pressure field, which includes a zero-crossing in its radial profiles, displays larger wavelengths than the hydrodynamic pressure field, correlates better with the near-field pressure signal and captures the radiated component of noise, especially at shallow angles. These properties make it a suitable field for informing pressure-based wavepacket models for jet noise.The influence of invariant solutions on the transient behaviour of an air bubble in a Hele-Shaw channelhttps://www.zbmath.org/1472.761062021-11-25T18:46:10.358925Z"Keeler, Jack S."https://www.zbmath.org/authors/?q=ai:keeler.jack-s"Thompson, Alice B."https://www.zbmath.org/authors/?q=ai:thompson.alice-b"Lemoult, Grégoire"https://www.zbmath.org/authors/?q=ai:lemoult.gregoire"Juel, Anne"https://www.zbmath.org/authors/?q=ai:juel.anne"Hazel, Andrew L."https://www.zbmath.org/authors/?q=ai:hazel.andrew-lSummary: We hypothesize that dynamical systems concepts used to study the transition to turbulence in shear flows are applicable to other transition phenomena in fluid mechanics. In this paper, we consider a finite air bubble that propagates within a Hele-Shaw channel containing a depth-perturbation. Recent experiments revealed that the bubble shape becomes more complex, quantified by an increasing number of transient bubble tips, with increasing flow rate. Eventually, the bubble changes topology, breaking into multiple distinct entities with non-trivial dynamics. We demonstrate that qualitatively similar behaviour to the experiments is exhibited by a previously established, depth-averaged mathematical model and arises from the model's intricate solution structure. For the bubble volumes studied, a stable asymmetric bubble exists for all flow rates of interest, while a second stable solution branch develops above a critical flow rate and transitions between symmetric and asymmetric shapes. The region of bistability is bounded by two Hopf bifurcations on the second branch. By developing a method for a numerical weakly nonlinear stability analysis we show that unstable periodic orbits (UPOs) emanate from the first Hopf bifurcation. Moreover, as has been found in shear flows, the UPOs are edge states that influence the transient behaviour of the system.On the role of bulk viscosity in compressible reactive shear layer developmentshttps://www.zbmath.org/1472.761242021-11-25T18:46:10.358925Z"Boukharfane, Radouan"https://www.zbmath.org/authors/?q=ai:boukharfane.radouan"Martínez Ferrer, Pedro José"https://www.zbmath.org/authors/?q=ai:martinez-ferrer.pedro-jose"Mura, Arnaud"https://www.zbmath.org/authors/?q=ai:mura.arnaud"Giovangigli, Vincent"https://www.zbmath.org/authors/?q=ai:giovangigli.vincentSummary: Despite 150 years of research after the reference work of Stokes, it should be acknowledged that some confusion still remains in the literature regarding the importance of bulk viscosity effects in flows of both academic and practical interests. On the one hand, it can be readily shown that the neglection of bulk viscosity (i.e., \(\kappa = 0\)) is strictly exact for mono-atomic gases. The corresponding bulk viscosity effects are also unlikely to alter the flowfield dynamics provided that the ratio of the shear viscosity \(\mu\) to the bulk viscosity \(\kappa\) remains sufficiently large. On the other hand, for polyatomic gases, the scattered available experimental and numerical data show that it is certainly not zero and actually often far from negligible. Therefore, since the ratio \(\kappa / \mu\) can display significant variations and may reach very large values (it can exceed thirty for dihydrogen), it remains unclear to what extent the neglection of \(\kappa\) holds. The purpose of the present study is thus to analyze the mechanisms through which bulk viscosity and associated processes may alter a canonical turbulent flow. In this context, we perform direct numerical simulations (DNS) of spatially-developing compressible non-reactive and reactive hydrogen-air shear layers interacting with an oblique shock wave. The corresponding flowfield is of special interest for various reactive high-speed flow applications, e.g., scramjets. The corresponding computations either neglect the influence of bulk viscosity (\(\kappa = 0\)) or take it into consideration by evaluating its value using the library. The qualitative inspection of the results obtained for two-dimensional cases in either the presence or the absence of bulk viscosity effects shows that the local and instantaneous structure of the mixing layer may be deeply altered when taking bulk viscosity into account. This contrasts with some mean statistical quantities, e.g., the vorticity thickness growth rate, which do not exhibit any significant sensitivity to the bulk viscosity. Enstrophy, Reynolds stress components, and turbulent kinetic energy (TKE) budgets are then evaluated from three-dimensional reactive simulations. Slight modifications are put into evidence on the energy transfer and dissipation contributions. From the obtained results, one may expect that refined large-eddy simulations (LES) may be rather sensitive to the consideration of bulk viscosity, while Reynolds-averaged Navier-Stokes (RANS) simulations, which are based on statistical averages, are not.Mechanics of bed particle saltation in turbulent wall-shear flowhttps://www.zbmath.org/1472.860072021-11-25T18:46:10.358925Z"Padhi, Ellora"https://www.zbmath.org/authors/?q=ai:padhi.ellora"Ali, Sk Zeeshan"https://www.zbmath.org/authors/?q=ai:ali.sk-zeeshan"Dey, Subhasish"https://www.zbmath.org/authors/?q=ai:dey.subhasishSummary: In this paper, we explore the mechanics of bed particle saltation in turbulent wall-shear flow, analysing the forces on a particle to perform saltation. The hydrodynamic drag encompasses the form drag and turbulent drag. The hydrodynamic lift comprises the Saffman lift, Magnus lift and turbulent lift. The subtle role of the Basset force in governing the particle trajectory is accounted for in the analysis. The bedload flux, emanating from the mathematical analysis of bed particle saltation, is determined. The results reveal that for the particle parameter range 20-100, the transport stage function equalling unity corroborates the threshold of bed particle saltation, where the saltation height and length are 1.3 and 9 times the particle size. For a given transport stage function, the relative saltation height and length decrease with an increase in particle parameter. For the particle parameter range 20-100, the relative saltation height and length increase with an increase in transport stage function, reaching their peaks, and then, they decrease. For a given particle parameter, the peak and mean particle densimetric Froude numbers increase as the transport stage function increases. The bedload flux curves for particle parameters 26 and 63 produce the upper and lower bound curves, respectively.