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Showing papers on "K-epsilon turbulence model published in 2015"


Journal ArticleDOI
TL;DR: A review of the problems and successes of computing turbulent flow can be found in this paper, where the authors provide the interested reader with most of the appropriate sources of turbulence modelling, exhibiting either as much detail as it is possible, by means of bibliography, or illustrating some of the most recent developments on the numerical modelling of turbulent flows.

357 citations


Journal ArticleDOI
TL;DR: In this paper, the Richardson-Kolmogorov equilibrium cascade is intimately linked to the dissipation scaling of turbulent eddies, and it is shown that a significant nonequilibrium region exists in various turbulent flows in which the energy spectrum has Kolmogorski's −5/3 wave number scaling over a wide wave-number range, yet C� ∼ Re m /Re n,w ithm ≈ 1 ≈ n, Re I a global/inlet Reynolds number and ReL a local turbulence Reynolds number.
Abstract: This article reviews evidence concerning the cornerstone dissipation scaling of turbulence theory: � = CU 3 /L, with C� = const., � the dissipation rate of turbulent kinetic energy U 2 ,a ndL an integral length scale characterizing the energy-containing turbulent eddies. This scaling is intimately linked to the Richardson-Kolmogorov equilibrium cascade. Accumulating evidence shows that a significant nonequilibrium region exists in various turbulent flows in which the energy spectrum has Kolmogorov's −5/3 wave-number scaling over a wide wave-number range, yet C� ∼ Re m /Re n ,w ithm ≈ 1 ≈ n, Re I a global/inlet Reynolds number, and ReL a local turbulence Reynolds number.

321 citations


Journal ArticleDOI
22 Oct 2015-Nature
TL;DR: A bifurcation scenario is uncovered that explains the transformation to fully turbulent pipe flow and the front dynamics of the different states encountered in the process and is bridged between understanding of the onset of turbulence and fully turbulent flows.
Abstract: Over a century of research into the origin of turbulence in wall-bounded shear flows has resulted in a puzzling picture in which turbulence appears in a variety of different states competing with laminar background flow. At moderate flow speeds, turbulence is confined to localized patches; it is only at higher speeds that the entire flow becomes turbulent. The origin of the different states encountered during this transition, the front dynamics of the turbulent regions and the transformation to full turbulence have yet to be explained. By combining experiments, theory and computer simulations, here we uncover a bifurcation scenario that explains the transformation to fully turbulent pipe flow and describe the front dynamics of the different states encountered in the process. Key to resolving this problem is the interpretation of the flow as a bistable system with nonlinear propagation (advection) of turbulent fronts. These findings bridge the gap between our understanding of the onset of turbulence and fully turbulent flows.

175 citations


Journal ArticleDOI
TL;DR: Capecelatro et al. as mentioned in this paper explored the fundamental modeling aspects related to multiphase turbulence, including the mechanisms responsible for generating volume fraction fluctuations, how energy is transferred between the phases, and how the cluster size distribution scales with various flow parameters.
Abstract: At sufficient mass loading and in the presence of a mean body force (e.g. gravity), an initially random distribution of particles may organize into dense clusters as a result of momentum coupling with the carrier phase. In statistically stationary flows, fluctuations in particle concentration can generate and sustain fluid-phase turbulence, which we refer to as cluster-induced turbulence (CIT). This work aims to explore such flows in order to better understand the fundamental modelling aspects related to multiphase turbulence, including the mechanisms responsible for generating volume-fraction fluctuations, how energy is transferred between the phases, and how the cluster size distribution scales with various flow parameters. To this end, a complete description of the two-phase flow is presented in terms of the exact Reynolds-average (RA) equations, and the relevant unclosed terms that are retained in the context of homogeneous gravity-driven flows are investigated numerically. An Eulerian–Lagrangian computational strategy is used to simulate fully developed CIT for a range of Reynolds numbers, where the production of fluid-phase kinetic energy results entirely from momentum coupling with finite-size inertial particles. The adaptive filtering technique recently introduced in our previous work (Capecelatro et al., J. Fluid Mech., vol. 747, 2014, R2) is used to evaluate the Lagrangian data as Eulerian fields that are consistent with the terms appearing in the RA equations. Results from gravity-driven CIT show that momentum coupling between the two phases leads to significant differences from the behaviour observed in very dilute systems with one-way coupling. In particular, entrainment of the fluid phase by clusters results in an increased mean particle velocity that generates a drag production term for fluid-phase turbulent kinetic energy that is highly anisotropic. Moreover, owing to the compressibility of the particle phase, the uncorrelated components of the particle-phase velocity statistics are highly non-Gaussian, as opposed to systems with one-way coupling, where, in the homogeneous limit, all of the velocity statistics are nearly Gaussian. We also observe that the particle pressure tensor is highly anisotropic, and thus additional transport equations for the separate contributions to the pressure tensor (as opposed to a single transport equation for the granular temperature) are necessary in formulating a predictive multiphase turbulence model.

136 citations


Journal ArticleDOI
TL;DR: In this article, a review of wave-turbulence interactions in stable atmospheric boundary layer (SABL) flows is presented, focusing on the nocturnal SABL.
Abstract: Flow in a stably stratified environment is characterized by anisotropic and intermittent turbulence and wavelike motions of varying amplitudes and periods. Understanding turbulence intermittency and wave-turbulence interactions in a stably stratified flow remains a challenging issue in geosciences including planetary atmospheres and oceans. The stable atmospheric boundary layer (SABL) commonly occurs when the ground surface is cooled by longwave radiation emission such as at night over land surfaces, or even daytime over snow and ice surfaces, and when warm air is advected over cold surfaces. Intermittent turbulence intensification in the SABL impacts human activities and weather variability, yet it cannot be generated in state-of-the-art numerical forecast models. This failure is mainly due to a lack of understanding of the physical mechanisms for seemingly random turbulence generation in a stably stratified flow, in which wave-turbulence interaction is a potential mechanism for turbulence intermittency. A workshop on wave-turbulence interactions in the SABL addressed the current understanding and challenges of wave-turbulence interactions and the role of wavelike motions in contributing to anisotropic and intermittent turbulence from the perspectives of theory, observations, and numerical parameterization. There have been a number of reviews on waves, and a few on turbulence in stably stratified flows, but not much on wave-turbulence interactions. This review focuses on the nocturnal SABL; however, the discussions here on intermittent turbulence and wave-turbulence interactions in stably stratified flows underscore important issues in stably stratified geophysical dynamics in general.

123 citations


Journal ArticleDOI
TL;DR: In this paper, the authors investigated the effect of super-hydrophobic (SH) surface micro-patterns on the dynamics of turbulent flow in the SH channel and found that between 80% and 100% of the DR in turbulent flow arises from the effective slip on the walls.
Abstract: The mechanism of turbulent drag reduction (DR) with super-hydrophobic (SH) surfaces is investigated by direct numerical simulation (DNS) and analysis of the governing equations in channel flow. The DNS studies were performed using lattice Boltzmann methods in channels with ‘idealized’ SH surfaces on both walls, comprised of longitudinal micro-grooves (MG), transverse MG, or micro-posts. DRs of to , to , and to were realized in DNS with longitudinal MG, transverse MG, and micro-posts, respectively. By mathematical analysis of the governing equations, it is shown that, in SH channel flows with any periodic SH micro-pattern on the walls, the magnitude of DR can be expressed as , where the first term represents the DR resulting from the effective slip on the walls, and the second term represents the DR or drag increase (DI) resulting from modifications to the turbulence dynamics and any secondary mean flows established in the SH channel compared to a channel flow with no-slip walls at the same bulk Reynolds number as the SH channel. Comparison of this expression to DNS results shows that, with all SH surface micro-patterns studied, between 80 % and 100 % of the DR in turbulent flow arises from the effective slip on the walls. Modifications to the turbulence dynamics contribute no more than 20 % of the total DR with longitudinal MG or micro-posts of high shear-free fraction (SFF), and a DI with transverse MG or micro-posts of moderate SFF. The effect of the SH surface on the normalized dynamics of turbulence is found to be small in all cases, and confined to additional production of turbulence kinetic energy (TKE) within a thin ‘surface layer’ of thickness of the order of the width of surface micro-indentations. Outside of this ‘surface layer’, the normalized dynamics of turbulence proceeds as in a turbulent channel flow with no-slip walls at the friction Reynolds number of the SH channel flow.

110 citations


Journal ArticleDOI
TL;DR: In this paper, the authors investigated the transient simulation of large scale bubbly flow in bubble columns using the unsteady Reynolds averaged Navier Stokes (URANS) equations and showed that a simulation time, time step length and mesh independent solution can be obtained for complex bubble flows using URANS equations under certain requirements.

93 citations


Journal ArticleDOI
TL;DR: In this article, a review of recent results for rotating turbulence, from several numerical and experimental researches, and in relation with theory and models, mostly for homogeneous flows, is presented.
Abstract: Rotating turbulence is a fundamental phenomenon appearing in several geophysical and industrial applications. Its study benefited from major advances in the recent years, but also raised new questions. We review recent results for rotating turbulence, from several numerical and experimental researches, and in relation with theory and models, mostly for homogeneous flows. We observe a convergence in the statistical description of rotating turbulence from the advent of modern experimental techniques and computational power that allows to investigate the structure and dynamics of rotating flows at similar parameters and with similar description levels. The improved picture about the anisotropization mechanisms, however, reveals subtle differences in the flow conditions, including its generation and boundary conditions, which lead to separate points of view about the role of linear mechanisms—the Coriolis force and inertial waves—compared with more complex nonlinear triadic interactions. This is discussed in relation with the most recent diagnostic of dynamical equations in physical and spectral space. [DOI: 10.1115/1.4029006]

90 citations


Journal ArticleDOI
TL;DR: In this paper, the authors describe a technique, using thin lines of triplet-state molecular tracers created by femtosecond-laser field ionization of helium atoms, for visualizing the flow of the normal fluid in superfluid liquid.
Abstract: We describe a technique, using thin lines of triplet-state $\mathrm{He}_{2}^{*}$ molecular tracers created by femtosecond-laser field ionization of helium atoms, for visualizing the flow of the normal fluid in superfluid $^{4}\mathrm{He}$, together with its application to thermal counterflow in a channel. We show that, at relatively small velocities, where the superfluid is already turbulent, the flow of the normal fluid remains laminar, but with a distorted velocity profile, while at a higher velocity there is a transition to turbulence. The form of the structure function in this turbulent state differs significantly from that found in types of conventional turbulence. This visualization technique also promises to be applicable to other fluid dynamical problems involving cryogenic helium.

85 citations


Journal ArticleDOI
TL;DR: In this paper, a high fidelity approach for wind turbine aero-elastic simulations including explicit representation of the atmospheric wind turbulence is presented, which uses a dynamic overset computational fluid dynamics (CFD) code for the aerodynamics coupled with a multi-body dynamics (MBD) for the motion responses to the aerodynamic loads.

84 citations


Journal ArticleDOI
TL;DR: In this paper, the ability of a two-fluid Eulerian-Eulerian computational multiphase fluid dynamic model to predict bubbly air-water flows is studied.

Journal ArticleDOI
TL;DR: In this paper, the authors focus on a model problem which allows them to address the fundamental fluid mechanics that is expected to be characteristic of the oceanographic regime and demonstrate that the oceanographically expected high value of the Prandtl number has a profound influence on the nature of the secondary instabilities that govern the transition process.
Abstract: Motivated by the importance of small-scale turbulent diapycnal mixing to the closure of the large-scale meridional overturning circulation (MOC) of the oceans, we focus on a model problem which allows us to address the fundamental fluid mechanics that is expected to be characteristic of the oceanographic regime. Our model problem is one in which the initial conditions consist of a stably stratified parallel shear flow which evolves into the turbulent regime through the growth of a Kelvin–Helmholtz wave to finite amplitude followed by transition to turbulence. Through both linear stability analysis and direct numerical simulations (DNS), we investigate the secondary instabilities and the turbulent mixing at a fixed high Reynolds number and for a range of Prandtl numbers. We demonstrate that the oceanographically expected high value of the Prandtl number has a profound influence on the nature of the secondary instabilities that govern the transition process. Specifically through non-separable linear stability analysis, we discover new characteristics for the shear-aligned convective instability such that it is modified into a mixed mode that is driven both by static instability and by shear. The growth rate and ultimate strength of this mode are both strongly enhanced at higher while the growth rate and ultimate strength of the stagnation point instability (SPI), which may compete for control of the transition process, are simultaneously impeded. Of equal importance is the fact that, for higher , the characteristic length scales associated with the dominant mixed mode of instability decrease and therefore there ceases to be a strong scale selectivity. In the limit of much higher , we conjecture that a wide range of spatial scales become equally unstable so as to support an ‘ultraviolet catastrophe’, in which a direct injection of energy occurs into a broad range of scales simultaneously. We further establish the validity of these analytical results through a series of computationally challenging DNS analyses, and provide a detailed analysis of the efficiency of the turbulent mixing of the density field that occurs subsequent to transition and of the entrainment of fluid into the mixing layer from the high-speed flanks of the shear flow. We show that the mixing efficiency decreases monotonically with increase of the molecular value of the Prandtl number and the expansion of the shear layer is reduced as such entrainment diminishes.

Journal ArticleDOI
TL;DR: In this paper, the authors used direct numerical simulation (DNS) calculations to determine the real size of turbulent eddies in a porous medium, thus avoiding turbulence modelling of any kind.
Abstract: When a turbulent flow in a porous medium is determined numerically, the crucial question is whether turbulence models should account only for turbulent structures restricted in size to the pore scale or whether the size of turbulent structures could exceed the pore scale. The latter would mean the existence of macroscopic turbulence in porous media, when turbulent eddies exceed the pore size. In order to determine the real size of turbulent structures in a porous medium, we simulated the turbulent flow by direct numerical simulation (DNS) calculations, thus avoiding turbulence modelling of any kind. With this study, which for the first time uses DNS calculations, we provide benchmark data for turbulent flow in porous media. Since perfect DNS calculations require the resolution of scales down to the Kolmogorov scale, often only approximate DNS solutions can be obtained, especially for high Reynolds numbers. This is accounted for by using and comparing two different DNS approaches, a finite volume method (FVM) with grid refinement towards the wall and a lattice Boltzmann method (LBM) with equal grid distribution. The solid matrix was simulated by a large number of rectangular bars arranged periodically. The number of bars in the solution domain with periodic boundary conditions was reduced systematically until a minimum size was found that does not suppress any large-scale turbulent structures. Two-point correlations, integral length scales and energy spectra were determined in order to answer the question of whether or not macroscopic turbulence can be found in porous media.

Journal ArticleDOI
TL;DR: The high-Reynolds-number limit of the grid-turbulence wind-tunnel experiment is concerned, and it is observed that the decay rate is Reynolds-number independent, which contradicts some models and supports others.
Abstract: Using the unique capabilities of the Variable Density Turbulence Tunnel at the Max Planck Institute for Dynamics and Self-Organization, we investigated virtually homogeneous and isotropic grid turbulence over a wide range of Reynolds numbers, Re = UM= , between 10 4 and 5 10 6 . The choice of pressurizable Sulfur Hexafluoride as a working gas makes it possible to reach extremely high Reynolds numbers without changing boundary conditions. Indeed, the Reynolds number we reached were higher than any previous classical grid wind-tunnel experiment. In this talk, we focus on the fundamental question of how fast turbulent energy decays once it has been created, and show that the Reynolds number plays no important role in setting the decay rate if it is high enough.

Journal ArticleDOI
TL;DR: In this article, an instability-sensitive, eddy-resolving turbulence model on the Second-Moment Closure level is proposed, which is based on the Unsteady RANS (Reynolds-Averaged Navier Stokes) framework.

Journal ArticleDOI
TL;DR: This paper presents a scale-dependent saturation model based on an effective turbulent resistivity which is determined by the turnover time scale of turbulent eddies and the magnetic energy density, and finds saturation levels between 43.8% and 1.3% for Pm≪1 and between 2.43% and 0.135%, respectively.
Abstract: The origin of strong magnetic fields in the Universe can be explained by amplifying weak seed fields via turbulent motions on small spatial scales and subsequently transporting the magnetic energy to larger scales. This process is known as the turbulent dynamo and depends on the properties of turbulence, i.e., on the hydrodynamical Reynolds number and the compressibility of the gas, and on the magnetic diffusivity. While we know the growth rate of the magnetic energy in the linear regime, the saturation level, i.e., the ratio of magnetic energy to turbulent kinetic energy that can be reached, is not known from analytical calculations. In this paper we present a scale-dependent saturation model based on an effective turbulent resistivity which is determined by the turnover time scale of turbulent eddies and the magnetic energy density. The magnetic resistivity increases compared to the Spitzer value and the effective scale on which the magnetic energy spectrum is at its maximum moves to larger spatial scales. This process ends when the peak reaches a characteristic wave number k☆ which is determined by the critical magnetic Reynolds number. The saturation level of the dynamo also depends on the type of turbulence and differs for the limits of large and small magnetic Prandtl numbers Pm. With our model we find saturation levels between 43.8% and 1.3% for Pm≫1 and between 2.43% and 0.135% for Pm≪1, where the higher values refer to incompressible turbulence and the lower ones to highly compressible turbulence.

Journal ArticleDOI
TL;DR: The Elliptic Blending Reynolds Stress Model (EB-RSM) has been subject to various modifications by several authors during the last decade, mainly for numerical robustness reasons as discussed by the authors.

Journal ArticleDOI
TL;DR: In this paper, the authors used an acoustic Doppler velocimeter in Puget Sound, WA to perform a detailed characterization of the turbulent flow encountered by a turbine in a tidal strait.

Journal ArticleDOI
TL;DR: It is argued that the linear and nonlinear dynamics of Alfvén waves are responsible, at a very fundamental level, for some of the key qualitative features of plasma turbulence that distinguish it from hydrodynamic turbulence, including the anisotropic cascade of energy and the development of current sheets at small scales.
Abstract: A dynamical approach, rather than the usual statistical approach, is taken to explore the physical mechanisms underlying the nonlinear transfer of energy, the damping of the turbulent fluctuations, and the development of coherent structures in kinetic plasma turbulence. It is argued that the linear and nonlinear dynamics of Alfven waves are responsible, at a very fundamental level, for some of the key qualitative features of plasma turbulence that distinguish it from hydrodynamic turbulence, including the anisotropic cascade of energy and the development of current sheets at small scales. The first dynamical model of kinetic turbulence in the weakly collisional solar wind plasma that combines self-consistently the physics of Alfven waves with the development of small-scale current sheets is presented and its physical implications are discussed. This model leads to a simplified perspective on the nature of turbulence in a weakly collisional plasma: the nonlinear interactions responsible for the turbulent cascade of energy and the formation of current sheets are essentially fluid in nature, while the collisionless damping of the turbulent fluctuations and the energy injection by kinetic instabilities are essentially kinetic in nature.

Journal ArticleDOI
TL;DR: In this paper, large eddy simulations (LES) of downbursts impinging over four different exposures namely open, countryside, suburban and urban, are performed, where ground surface roughness is simulated using fractal surfaces generated by random Fourier modes (RFM).

Journal ArticleDOI
TL;DR: In this paper, particle image velocimetry (PIV) measurements of various terms of the nonhomogeneous Karman-Howarth-Monin equation in the most inhomogeneous and anisotropic region of grid-generated turbulence, the production region which lies between the grid and the peak of turbulence intensity.
Abstract: We perform particle image velocimetry (PIV) measurements of various terms of the non-homogeneous Karman–Howarth–Monin equation in the most inhomogeneous and anisotropic region of grid-generated turbulence, the production region which lies between the grid and the peak of turbulence intensity. We use a well-documented fractal grid which is known to magnify the streamwise extent of the production region and abate its turbulence activity. On the centreline around the centre of that region the two-point advection and transport terms are dominant and the production is significant too. It is therefore impossible to apply usual Kolmogorov arguments based on the Karman–Howarth–Monin equation and resulting dimensional considerations to deduce interscale flux and spectral properties. The interscale energy transfers at this location turn out to be highly anisotropic and consist of a combined forward and inverse cascade in different directions which, when averaged over directions, gives an interscale energy flux that is negative (hence forward cascade on average) and not too far from linear in , the modulus of the separation vector between two points. The energy spectrum of the streamwise fluctuating component exhibits a well-defined power law over one decade, even though the streamwise direction is at a small angle to the inverse cascading direction.

Journal ArticleDOI
TL;DR: In this article, two separate large eddy simulations are carried out to investigate the effects of accurate computation of the curvilinear water-surface deformation of the flow through a bridge contraction.
Abstract: Two separate large eddy simulations (LES) are carried out to investigate the effects of accurate computation of the curvilinear water-surface deformation of the flow through a bridge contraction. One LES employs the rigid-lid boundary condition at the water surface, while the other uses a highly accurate level-set method (LSM), which allows the water surface to adjust itself freely in response to the flow. The simulation with the LSM is validated with data from complementary physical model tests under analogous geometrical and flow conditions. Streamwise velocity, bed-shear stress and second-order turbulence statistics obtained from both simulations are compared, and it is shown that the turbulence structure of this flow is influenced strongly by the water-surface deformation. While bed-shear stresses and first-order statistics are very similar for both cases, the instantaneous turbulence structure and consequently, the second-order statistics, are distinctly different. The correct prediction of the water-surface deformation of such flows is deemed important for the accuracy of their simulation. Read More: http://ascelibrary.org/doi/10.1061/%28ASCE%29HY.1943-7900.0001028

Journal ArticleDOI
TL;DR: In this article, the authors show that the typical flow structures appearing in transitional channel flows at moderate Reynolds numbers are not spots but isolated turbulent bands, which have much longer lifetimes than the spots.
Abstract: In this letter, we show via numerical simulations that the typical flow structures appearing in transitional channel flows at moderate Reynolds numbers are not spots but isolated turbulent bands, which have much longer lifetimes than the spots. Localized perturbations can evolve into isolated turbulent bands by continuously growing obliquely when the Reynolds number is larger than 660. However, interactions with other bands and local perturbations cause band breaking and decay. The competition between the band extension and breaking does not lead to a sustained turbulence until Re becomes larger than about 1000. Above this critical value, the bands split, providing an effective mechanism for turbulence spreading.

Journal ArticleDOI
TL;DR: Two theoretical atmosphere refractive-index fluctuations spectral models are derived for optical waves propagating through anisotropic non-Kolmogorov atmospheric turbulence and expressions for the variance of angle of arrival (AOA) fluctuations are derived.
Abstract: Theoretical and experimental investigations have shown that the atmospheric turbulence exhibits both anisotropic and non-Kolmogorov properties. In this work, two theoretical atmosphere refractive-index fluctuations spectral models are derived for optical waves propagating through anisotropic non-Kolmogorov atmospheric turbulence. They consider simultaneously the finite turbulence inner and outer scales and the asymmetric property of turbulence eddies in the orthogonal xy-plane throughout the path. Two anisotropy factors which parameterize the asymmetry of turbulence eddies in both horizontal and vertical directions are introduced in the orthogonal xy-plane, so that the circular symmetry assumption of turbulence eddies in the xy-plane is no longer required. Deviations from the classic 11/3 power law behavior in the spectrum model are also allowed by assuming power law value variations between 3 and 4. Based on the derived anisotropic spectral model and the Rytov approximation theory, expressions for the variance of angle of arrival (AOA) fluctuations are derived for optical plane and spherical waves propagating through weak anisotropic non-Kolmogorov turbulence. Calculations are performed to analyze the derived spectral models and the variance of AOA fluctuations.

Journal ArticleDOI
TL;DR: An efficient, higher order method for fast calculation of an ensemble of solutions of the Navier–Stokes equations and a complete stability and convergence analysis of the method for laminar flows and an extension to turbulent flows is given.
Abstract: This report presents an efficient, higher order method for fast calculation of an ensemble of solutions of the Navier---Stokes equations. We give a complete stability and convergence analysis of the method for laminar flows and an extension to turbulent flows. For high Reynolds number flows, we propose and analyze an eddy viscosity model with a recent reparameterization of the mixing length. This turbulence model depends on an ensemble mean compatible with the higher order method. We show the turbulence model has superior stability, also demonstrated in numerical tests. We also give tests showing the potential of the new method for exploring flow problems to compute turbulence intensities, effective Lyapunov exponents, windows of predictability and to verify the selective decay principle.

Journal ArticleDOI
TL;DR: In this paper, a critical assessment of the widely used Thorpe-scale method, which is used to estimate dissipation and mixing rates in stratified turbulent flows from density measurements along vertical profiles, is provided.
Abstract: This paper uses the energetics framework developed by Scotti and White to provide a critical assessment of the widely used Thorpe-scale method, which is used to estimate dissipation and mixing rates in stratified turbulent flows from density measurements along vertical profiles. This study shows that the relevant displacement scale in general is not the rms value of the Thorpe displacement. Rather, the displacement field must be Reynolds decomposed to separate the mean from the turbulent component, and it is the turbulent component that ought to be used to diagnose mixing and dissipation. In general, the energetics of mixing in an overall stably stratified flow involves potentially complex exchanges among the available potential energy and kinetic energy associated with the mean and turbulent components of the flow. The author considers two limiting cases: shear-driven mixing, where mixing comes at the expense of the mean kinetic energy of the flow, and convective-driven mixing, which taps the ava...

Journal ArticleDOI
TL;DR: In this paper, a three-dimensional numerical simulation is used to investigate intermittency in incompressible weak magnetohydrodynamic turbulence with a strong uniform magnetic field and zero cross-helicity.
Abstract: Three-dimensional numerical simulation is used to investigate intermittency in incompressible weak magnetohydrodynamic turbulence with a strong uniform magnetic field and zero cross-helicity. At leading order, this asymptotic regime is achieved via three-wave resonant interactions with the scattering of a wave on a 2D mode for which . When the interactions with the 2D modes are artificially reduced, we show numerically that the system exhibits an energy spectrum with , whereas the expected exact solution with is recovered with the full nonlinear system. In the latter case, strong intermittency is found when the vector separation of structure functions is taken transverse to . This result may be explained by the influence of the 2D modes whose regime belongs to strong turbulence. In addition to shedding light on the origin of this intermittency, we derive a log-Poisson law, , which fits the data perfectly and highlights the important role of parallel current sheets.

Book ChapterDOI
01 Jan 2015
TL;DR: In this paper, the authors study the ordering of forces in the Earth's core at all scales and introduce tau-ell regime diagrams, which represent how timescales tau and length scales ell are related to the various relevant physical phenomena.
Abstract: Flows in natural systems are usually turbulent. The core of the Earth makes no exception. However, turbulence in the core departs from classical hydrodynamic turbulence because of the presence of a strong magnetic field and rotation. In this chapter, we work out how these two ingredients alter the organization of turbulence, and build plausible scenarios for turbulence in planetary cores. We recall basics of classical turbulence and review various tools that are used to study turbulence. Turbulence involves a wide range of spatial and temporal scales. Forces that dominate at a given scale become unimportant at other scales. We carefully analyse the ordering of forces in the Earth’s core at all scales. We introduce tau-ell regime diagrams, which represent how timescales tau and length scales ell are related to the various relevant physical phenomena. Using these diagrams, we investigate step by step the different turbulent regimes that can take place. Our analysis emphasizes the role of rotation in limiting magnetic dissipation.

Journal ArticleDOI
TL;DR: In this article, the authors assess the accuracy of ILES using numerical methods most commonly employed in computational astrophysics by means of a number of local simulations of driven, weakly compressible, anisotropic turbulence.
Abstract: In the implicit large eddy simulation (ILES) paradigm, the dissipative nature of high-resolution shock-capturing schemes is exploited to provide an implicit model of turbulence. The ILES approach has been applied to different contexts, with varying degrees of success. It is the de-facto standard in many astrophysical simulations and in particular in studies of core-collapse supernovae (CCSN). Recent 3D simulations suggest that turbulence might play a crucial role in core-collapse supernova explosions, however the fidelity with which turbulence is simulated in these studies is unclear. Especially considering that the accuracy of ILES for the regime of interest in CCSN, weakly compressible and strongly anisotropic, has not been systematically assessed before. Anisotropy, in particular, could impact the dissipative properties of the flow and enhance the turbulent pressure in the radial direction, favouring the explosion. In this paper we assess the accuracy of ILES using numerical methods most commonly employed in computational astrophysics by means of a number of local simulations of driven, weakly compressible, anisotropic turbulence. Our simulations employ several different methods and span a wide range of resolutions. We report a detailed analysis of the way in which the turbulent cascade is influenced by the numerics. Our results suggest that anisotropy and compressibility in CCSN turbulence have little effect on the turbulent kinetic energy spectrum and a Kolmogorov $k^{-5/3}$ scaling is obtained in the inertial range. We find that, on the one hand, the kinetic energy dissipation rate at large scales is correctly captured even at low resolutions, suggesting that very high “effective Reynolds number” can be achieved at the largest scales of the simulation. On the other hand, the dynamics at intermediate scales appears to be completely dominated by the so-called bottleneck effect, i.e., the pile up of kinetic energy close to the dissipation range due to the partial suppression of the energy cascade by numerical viscosity. An inertial range is not recovered until the point where high resolution ∼5123, which would be difficult to realize in global simulations, is reached. We discuss the consequences for CCSN simulations.

Journal ArticleDOI
TL;DR: In this article, a detailed analysis of the flow field of a straight and a slightly rotating turbulent free jet both experimentally and by means of CFD simulation with various turbulence models is presented.