Eddy Turnover Time Research Articles

SOME STARS ARE TOTALLY METAL: A NEW MECHANISM DRIVING DUST ACROSS STAR-FORMING CLOUDS, AND CONSEQUENCES FOR PLANETS, STARS, AND GALAXIES

Dust grains in neutral gas behave as aerodynamic particles, so they can develop large density fluctuations independent of gas density fluctuations. Specifically, gas turbulence can drive order-of-magnitude 'resonant' fluctuations in the dust on scales where the gas stopping/drag timescale is comparable to the turbulent eddy turnover time. Here we show that for large grains (size >0.1 micron, containing most grain mass) in sufficiently large molecular clouds (radii >1-10 pc, masses >10^4 M_sun), this scale becomes larger than the characteristic sizes of pre-stellar cores (the sonic length), so large fluctuations in the dust-to-gas ratio are imprinted on cores. As a result, star clusters and protostellar disks formed in large clouds should exhibit significant abundance spreads in the elements preferentially found in large grains. This naturally predicts populations of carbon-enhanced stars, certain highly unusual stellar populations observed in nearby open clusters, and may explain the 'UV upturn' in early-type galaxies. It will also dramatically change planet formation in the resulting protostellar disks, by preferentially 'seeding' disks with an enhancement in large carbonaceous or silicate grains. The relevant threshold for this behavior scales simply with cloud densities and temperatures, making straightforward predictions for clusters in starbursts and high-redshift galaxies. Because of the selective sorting by size, this process is not necessarily visible in extinction mapping. We also predict the shape of the abundance distribution -- when these fluctuations occur, a small fraction of the cores may actually be seeded with abundances ~100 times the mean, such that they are almost 'totally metal' (Z~1)! Assuming the cores collapse, these totally metal stars would be rare (1 in 10^4 in clusters where this occurs), but represent a fundamentally new stellar evolution channel.

The effect of viscoelasticity on the turbulent kinetic energy cascade

AbstractDirect numerical simulations of statistically steady homogeneous isotropic turbulence in viscoelastic fluids described by the FENE-P model, such as those laden with polymers, are presented. It is shown that the strong depletion of the turbulence dissipation reported by previous authors does not necessarily imply a depletion of the nonlinear energy cascade. However, for large relaxation times, of the order of the eddy turnover time, the polymers remove more energy from the large scales than they can dissipate and transfer the excess energy back into the turbulent dissipative scales. This is effectively a polymer-induced kinetic energy cascade which competes with the nonlinear energy cascade of the turbulence leading to its depletion. It is also shown that the total energy flux to the small scales from both cascade mechanisms remains approximately the same fraction of the kinetic energy over the turnover time as the nonlinear energy cascade flux in Newtonian turbulence.

Horizontal turbulent diffusion in a convective mixed layer

AbstractA large eddy simulation (LES) is used to estimate a reliable horizontal turbulent diffusion coefficient, $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}K_{{h}}$, in a convective mixed layer (CML). The introduction of a passive scalar field with a fixed horizontal gradient at a given time enables $K_{{h}}$ estimation as a function of height, based on the simulated turbulent horizontal scalar flux. Here $K_{{h}}$ is found to be of the order of $100\ {\mathrm{m}}^2\ {\mathrm{s}}^{-1}$ for a typical terrestrial atmospheric CML. It is shown to scale by the product of the CML convective velocity, $w_{*}$, and its depth, $h$. Here $K_{{h}}$ is characterized by a vertical profile in the CML: it is large near both the bottom and top of the CML, where horizontal flows associated with convection are large. The equation pertaining to the temporal rate of change of a horizontal scalar flux suggests that $K_{{h}}$ is determined by a balance between production and pressure correlation at a fully developed stage. Pressure correlation near the bottom of the CML is localized in convergence zones near the boundaries of convective cells and becomes large within an eddy turnover time, $h/w_{*}$, after the introduction of the passive scalar field.

Simulations of diesel–methanol dual-fuel engine combustion with large eddy simulation and Reynolds-averaged Navier–Stokes model

A comparison of large eddy simulation and Reynolds-averaged Navier–Stokes combustion models was performed using simulations of a diesel–methanol dual-fuel engine. The two models share the assumption that the reaction rate for each species is determined by the chemical kinetic processes as well as the relative magnitude of mixing and reaction effects, which are characterized by a kinetic timescale and a turbulence timescale. The main difference in the two models lies in their formulations of the turbulence timescale. The turbulence timescale in the Reynolds-averaged Navier–Stokes model is proportional to the eddy turnover time, while the turbulence timescale in the large eddy simulation model is the time needed for the mixture to reach perfectly mixed conditions based on the scalar dissipation rate. The models were tested using data from experiments on a modified heavy-duty diesel engine. Test cases using low methanol ratios, high methanol ratios and different initial temperatures were examined. In general, the ignition delay increases as the methanol ratio increases. In the models, this was found to occur due to the chemical interaction of the methanol and the diesel fuel. In addition, methanol auto-ignition occurs when the initial temperature is over 425 K. The large eddy simulation model and Reynolds-averaged Navier–Stokes model give similar predictions for the low methanol ratio cases. The large eddy simulation model shows improved capability to predict the high methanol ratio cases and methanol auto-ignition cases, represented by good agreement with experimental results.

THE MATRYOSHKA RUN: A EULERIAN REFINEMENT STRATEGY TO STUDY THE STATISTICS OF TURBULENCE IN VIRIALIZED COSMIC STRUCTURES

We study the statistical properties of turbulence driven by structure formation in a massive merging galaxy cluster at z=0. The development of turbulence is ensured as the largest eddy turnover time is much shorter than the Hubble time independent of mass and redshift. We achieve a large dynamic range of spatial scales through a novel Eulerian refinement strategy where the cluster volume is refined with progressively finer uniform nested grids during gravitational collapse. This provides an unprecedented resolution of 7.3 h^{-1} kpc across the virial volume. The probability density functions of various velocity derived quantities exhibit the features characteristic of fully developed compressible turbulence observed in dedicated periodic-box simulations. Shocks generate only 60% of the total vorticity within \rvir/3 region and 40% beyond that. We compute second and third order, longitudinal and transverse, structure functions for both solenoidal and compressional components, in the cluster core, virial region and beyond. The structure functions exhibit a well defined inertial range. The injection scale is comparable to the virial radius but increases towards the outskirts. Within \rvir/3, the spectral slope of the solenoidal component is close to Kolmogorov's, but for the compressional component is substantially steeper and close to Burgers'; the flow is mostly solenoidal and statistically rigorously consistent with fully developed, homogeneous and isotropic turbulence. Small scale anisotropy appears due to numerical artifact. Towards the virial region, the flow becomes compressional, the structure functions flatter and modest genuine anisotropy appear. In comparison, mesh adaptivity based on Lagrangian refinement and the same finest resolution, leads to lack of turbulent power on small scale and excess thereof on large scales, and unreliable density weighted structure functions.

The evolution of a stratified turbulent cloud

AbstractLocalized regions of turbulence, or turbulent clouds, in a stratified fluid are the subject of this study, which focuses on the edge dynamics occurring between the turbulence and the surrounding quiescent region. Through laboratory experiments and numerical simulations of stratified turbulent clouds, we confirm that the edge dynamics can be subdivided into materially driven intrusions and horizontally travelling internal wave-packets. Three-dimensional visualizations show that the internal gravity wave-packets are in fact large-scale pancake structures that grow out of the turbulent cloud into the adjacent quiescent region. The wave-packets were tracked in time, and it is found that their speed obeys the group speed relation for linear internal gravity waves. The energetics of the propagating waves, which include waveforms that are inclined with respect to the horizontal, are also considered and it is found that, after a period of two eddy turnover times, the internal gravity waves carry up to 16 % of the cloud kinetic energy into the initially quiescent region. Turbulent events in nature are often in the form of decaying turbulent clouds, and it is therefore suggested that internal gravity waves radiated from an initial cloud could play a significant role in the reorganization of energy and momentum in the atmosphere and oceans.

Turbulence structure and budgets in curved pipes

Turbulent flow in curved pipes was investigated by Direct Numerical Simulation. Three curvatures δ (pipe radius a/curvature radius c) were examined: δ=0 (straight pipe), simulated for validation and comparison purposes; δ=0.1; and δ=0.3. The friction velocity Reynolds number (based on the pipe radius a) was 500 in all cases, yielding bulk Reynolds numbers of ∼17,000, ∼15,000 and ∼12,000 for δ=0, 0.1 and 0.3, respectively. The computational domain was ten pipe radii in length and was resolved by up to 20×106 hexahedral finite volumes. The time step was chosen equal to a wall time unit; 1 Large Eddy TurnOver Time (LETOT) was thus resolved by 500 time steps and simulations were typically protracted for 20 LETOT’s, the last 10 being used to build turbulence statistics and budgets.In curved pipes, time mean results showed Dean circulation and a strong velocity stratification in the curvature direction, as in laminar flow; turbulent fluctuations were highest in the outer bend region, whereas the flow near the inner wall was almost laminar. Significant turbulence levels were confined to a near-wall layer narrower than in the straight pipe. Near-wall streamwise velocity and wall shear stress exhibited the streak structure typical of turbulent channel flows only along the outer wall, while on the inner wall they exhibited a flat and low-level distribution. As the curvature increased, fluctuations in the plane of the cross section increased in intensity, following the trend of the time mean secondary flow, whereas axial (streamwise) fluctuations became weaker. Overall turbulence levels decreased with the curvature and were lower in a curved pipe than in the straight pipe. Turbulence budgets over the cross section confirmed that in curved pipes production and other budget terms are comparable with those in the straight pipe (or even higher) in the outer bend region, whereas they rapidly decay as one moves towards the inner side. They also indicated that, in curved pipes, convection terms play a significant role in the turbulence budget, especially in the regions of the Dean vortices.

Spectral non-locality, absolute equilibria and Kraichnan–Leith–Batchelor phenomenology in two-dimensional turbulent energy cascades

AbstractWe study the degree to which Kraichnan–Leith–Batchelor (KLB) phenomenology describes two-dimensional energy cascades in$\alpha $turbulence, governed by$\partial \theta / \partial t+ J(\psi , \theta )= \nu {\nabla }^{2} \theta + f$, where$\theta = {(- \Delta )}^{\alpha / 2} \psi $is generalized vorticity, and$\hat {\psi } (\boldsymbol{k})= {k}^{- \alpha } \hat {\theta } (\boldsymbol{k})$in Fourier space. These models differ in spectral non-locality, and include surface quasigeostrophic flow ($\alpha = 1$), regular two-dimensional flow ($\alpha = 2$) and rotating shallow flow ($\alpha = 3$), which is the isotropic limit of a mantle convection model. We re-examine arguments for dual inverse energy and direct enstrophy cascades, including Fjørtoft analysis, which we extend to general$\alpha $, and point out their limitations. Using an$\alpha $-dependent eddy-damped quasinormal Markovian (EDQNM) closure, we seek self-similar inertial range solutions and study their characteristics. Our present focus is not on coherent structures, which the EDQNM filters out, but on any self-similar and approximately Gaussian turbulent component that may exist in the flow and be described by KLB phenomenology. For this, the EDQNM is an appropriate tool. Non-local triads contribute increasingly to the energy flux as$\alpha $increases. More importantly, the energy cascade is downscale in the self-similar inertial range for$2. 5\lt \alpha \lt 10$. At$\alpha = 2. 5$and$\alpha = 10$, the KLB spectra correspond, respectively, to enstrophy and energy equipartition, and the triad energy transfers and flux vanish identically. Eddy turnover time and strain rate arguments suggest the inverse energy cascade should obey KLB phenomenology and be self-similar for$\alpha \lt 4$. However, downscale energy flux in the EDQNM self-similar inertial range for$\alpha \gt 2. 5$leads us to predict that any inverse cascade for$\alpha \geq 2. 5$will not exhibit KLB phenomenology, and specifically the KLB energy spectrum. Numerical simulations confirm this: the inverse cascade energy spectrum for$\alpha \geq 2. 5$is significantly steeper than the KLB prediction, while for$\alpha \lt 2. 5$we obtain the KLB spectrum.

Time-resolved measurements of coherent structures in the turbulent boundary layer

Time-resolved particle image velocimetry was used to examine the structure and evolution of swirling coherent structure (SCS), one interpretation of which is a marker for a three-dimensional coherent vortex structure, in wall-parallel planes of a turbulent boundary layer with a large field of view, 4.3δ × 2.2δ. Measurements were taken at four different wall-normal locations ranging from y/δ = 0.08–0.48 at a friction Reynolds number, Re_τ = 410. The data set yielded statistically converged results over a larger field of view than typically observed in the literature. The method for identifying and tracking swirling coherent structure is discussed, and the resulting trajectories, convection velocities, and lifespan of these structures are analyzed at each wall-normal location. The ability of a model in which the entirety of an individual SCS travels at a single convection velocity, consistent with the attached eddy hypothesis of Townsend (The structure of turbulent shear flows. Cambridge University Press, Cambridge, 1976), to describe the data is investigated. A methodology for determining whether such structures are “attached” or “detached” from the wall is also proposed and used to measure the lifespan and convection velocity distributions of these different structures. SCS were found to persist for longer periods of time further from the wall, particularly those inferred to be “detached” from the wall, which could be tracked for longer than 5 eddy turnover times.

The small-scale dynamo: breaking universality at high Mach numbers

The small-scale dynamo plays a substantial role in magnetizing the Universe under a large range of conditions, including subsonic turbulence at low Mach numbers, highly supersonic turbulence at high Mach numbers and a large range of magnetic Prandtl numbers Pm, i.e. the ratio of kinetic viscosity to magnetic resistivity. Low Mach numbers may, in particular, lead to the well-known, incompressible Kolmogorov turbulence, while for high Mach numbers, we are in the highly compressible regime, thus close to Burgers turbulence. In this paper, we explore whether in this large range of conditions, universal behavior can be expected. Our starting point is previous investigations in the kinematic regime. Here, analytic studies based on the Kazantsev model have shown that the behavior of the dynamo depends significantly on Pm and the type of turbulence, and numerical simulations indicate a strong dependence of the growth rate on the Mach number of the flow. Once the magnetic field saturates on the current amplification scale, backreactions occur and the growth is shifted to the next-larger scale. We employ a Fokker–Planck model to calculate the magnetic field amplification during the nonlinear regime, and find a resulting power-law growth that depends on the type of turbulence invoked. For Kolmogorov turbulence, we confirm previous results suggesting a linear growth of magnetic energy. For more general turbulent spectra, where the turbulent velocity scales with the characteristic length scale as uℓ∝ℓϑ, we find that the magnetic energy grows as (t/Ted)2ϑ/(1−ϑ), with t being the time coordinate and Ted the eddy-turnover time on the forcing scale of turbulence. For Burgers turbulence, ϑ = 1/2, quadratic rather than linear growth may thus be expected, as the spectral energy increases from smaller to larger scales more rapidly. The quadratic growth is due to the initially smaller growth rates obtained for Burgers turbulence. Similarly, we show that the characteristic length scale of the magnetic field grows as t1/(1−ϑ) in the general case, implying t3/2 for Kolmogorov and t2 for Burgers turbulence. Overall, we find that high Mach numbers, as typically associated with steep spectra of turbulence, may break the previously postulated universality, and introduce a dependence on the environment also in the nonlinear regime.

An analytical study of the self-induced inviscid dynamics of two-dimensional uniform vortices

The self-induced dynamics of a uniform planar vortex in an isochoric, inviscid fluid is analytically investigated, by writing a new nonlinear integrodifferential problem which describes the time evolution of the Schwarz function of its boundary. In order to overcome the difficulties related to the nonlinear nature of the problem, an approximate solution of the above problem is proposed in terms of a hierarchy of linear integral equations. In particular, the solution at the first order is here investigated and applied to a class of uniform vortices, the kinematics of which is well known. A rich mathematical phenomenology has been found behind the approximate dynamics. In particular, the motion of certain branch points and the consequent changes in the algebraic structure of the Schwarz function appear to be its key features. The approximate solutions are finally compared with the contour dynamics simulations of the vortex motion. The agreement is satisfactory up to times of the order of a quarter of the eddy turnover time, while it becomes more and more qualitative at later times. Eventually, the physical meaning of the approximate solutions is lost, the corresponding vortex boundaries becoming non-simple curves.

THE IMPACT OF THERMODYNAMICS ON GRAVITATIONAL COLLAPSE: FILAMENT FORMATION AND MAGNETIC FIELD AMPLIFICATION

Stars form by the gravitational collapse of interstellar gas. The thermodynamic response of the gas can be characterized by an effective equation of state. It determines how gas heats up or cools as it gets compressed, and hence plays a key role in regulating the process of stellar birth on virtually all scales, ranging from individual star clusters up to the galaxy as a whole. We present a systematic study of the impact of thermodynamics on gravitational collapse in the context of high-redshift star formation, but argue that our findings are also relevant for present-day star formation in molecular clouds. We consider a polytropic equation of state, P = k rho^Gamma, with both sub-isothermal exponents Gamma < 1 and super-isothermal exponents Gamma > 1. We find significant differences between these two cases. For Gamma > 1, pressure gradients slow down the contraction and lead to the formation of a virialized, turbulent core. Weak magnetic fields are strongly tangled and efficiently amplified via the small-scale turbulent dynamo on timescales corresponding to the eddy-turnover time at the viscous scale. For Gamma < 1, on the other hand, pressure support is not sufficient for the formation of such a core. Gravitational contraction proceeds much more rapidly and the flow develops very strong shocks, creating a network of intersecting sheets and extended filaments. The resulting magnetic field lines are very coherent and exhibit a considerable degree of order. Nevertheless, even under these conditions we still find exponential growth of the magnetic energy density in the kinematic regime.

Long-time properties of magnetohydrodynamic turbulence and the role of symmetries

Using direct numerical simulations with grids of up to 512(3) points, we investigate long-time properties of three-dimensional magnetohydrodynamic turbulence in the absence of forcing and examine in particular the roles played by the quadratic invariants of the system and the symmetries of the initial configurations. We observe that when sufficient accuracy is used, initial conditions with a high degree of symmetries, as in the absence of helicity, do not travel through parameter space over time, whereas by perturbing these solutions either explicitly or implicitly using, for example, single precision for long times, the flows depart from their original behavior and can either become strongly helical or have a strong alignment between the velocity and the magnetic field. When the symmetries are broken, the flows evolve towards different end states, as already predicted by statistical arguments for nondissipative systems with the addition of an energy minimization principle. Increasing the Reynolds number by an order of magnitude when using grids of 64(3)-512(3) points does not alter these conclusions. Furthermore, the alignment properties of these flows, between velocity, vorticity, magnetic potential, induction, and current, correspond to the dominance of two main regimes, one helically dominated and one in quasiequipartition of kinetic and magnetic energies. We also contrast the scaling of the ratio of magnetic energy to kinetic energy as a function of wave number to the ratio of eddy turnover time to Alfvén time as a function of wave number. We find that the former ratio is constant with an approximate equipartition for scales smaller than the largest scale of the flow, whereas the ratio of time scales increases with increasing wave number.

ENHANCED DISSIPATION RATE OF MAGNETIC FIELD IN STRIPED PULSAR WINDS BY THE EFFECT OF TURBULENCE

In this letter we report on turbulent acceleration of the dissipation of magnetic field in the postshock re- gion of a Poynting flux-dominated flow, such as the Crab pulsar wind nebula. We have performed two- dimensional resistive relativistic magnetohydrodynamics simulations of subsonic turbulence driven by the Richtmyer-Meshkov instability at the shock fronts of the Poynting flux-dominated flows in pulsar winds. We find that turbulence stretches current sheets which substantially enhances the dissipation of magnetic field, and that most of the initial magnetic field energy is dissipated within a few eddy-turnover times. We also develop a simple analytical model for turbulent dissipation of magnetic field that agrees well with our simulations. The analytical model indicates that the dissipation rate does not depend on resistivity even in the small resistivity limit. Our findings can possibly alleviate the {\sigma}-problem in the Crab pulsar wind nebulae.

Isotropization at small scales of rotating helically driven turbulence

AbstractWe present numerical evidence of how three-dimensionalization occurs at small scale in rotating turbulence with Beltrami ($\mathit{ABC}$) forcing, creating helical flow. The Zeman scale ${\ell }_{\Omega } $ at which the inertial and eddy turn-over times are equal is more than one order of magnitude larger than the dissipation scale, with the relevant domains (large-scale inverse cascade of energy, dual regime in the direct cascade of energy $E$ and helicity $H$, and dissipation) each moderately resolved. These results stem from the analysis of a large direct numerical simulation on a grid of $307{2}^{3} $ points, with Rossby and Reynolds numbers, respectively, equal to $0. 07$ and $2. 7\ensuremath{\times} 1{0}^{4} $. At scales smaller than the forcing, a helical wave-modulated inertial law for the energy and helicity spectra is followed beyond ${\ell }_{\Omega } $ by Kolmogorov spectra for $E$ and $H$. Looking at the two-dimensional slow manifold, we also show that the helicity spectrum breaks down at ${\ell }_{\Omega } $, a clear sign of recovery of three-dimensionality in the small scales.

Arrays of vortices in shallow fluids: Three-dimensional structure and dispersion

The role of three-dimensional (3D) flow structures in an electromagnetically generated array of vortices in a single shallow (electrolytic) fluid layer with and without a vertical no-slip wall has been investigated by stereoscopic particle image velocimetry. This array of vortices is a result of a continuous, however, time-dependent periodic forcing. Additionally, the dispersion of passive tracers by this linear array of vortices is explored with 3D numerical simulations. As the parameter regime is quite extensive (fluid layer depth, current density, forcing frequency, etc.), we have restricted this study to two specific cases with a fixed fluid-layer depth: the quasi-two-dimensional (quasi-2D) laminar regime (low current density, or weak forcing) and a regime with substantial 3D secondary flows (high current density, or strong forcing). In all cases, the forcing frequency is taken similar to the typical eddy turnover time of the quasi-2D vortices. The low-forcing regime typically results in quasi-2D laminar flows which can hardly be considered turbulent. However, the compressible horizontal free-surface flow strongly affects the spatial distribution of passive tracers. The high-forcing regime gives rise to a strong inertia-dominated flow, including locally strong 3D secondary circulations and rapid vertical mixing of passive tracers, despite the shallowness of the fluid layer. Finally, the present investigation suggests that forcing too close to the vertical (no-slip) walls results in a substantial reduction of the horizontal integral length scale and enhanced production of small-scale 3D flows.

Studying Lagrangian dynamics of turbulence using on-demand fluid particle tracking in a public turbulence database

A recently developed public turbulence database system (http://turbulence.pha.jhu.edu) provides new ways to access large datasets generated from high-performance computer simulations of turbulent flows to perform numerical experiments. The database archives 10244 (spatial and time) data points obtained from a pseudo-spectral direct numerical simulation (DNS) of forced isotropic turbulence. The flow's Taylor-scale Reynolds number is Re λ=443, and the simulation output spans about one large-scale eddy turnover time. Besides the stored velocity and pressure fields, built-in first- and second-order space differentiation, as well as spatial and temporal interpolations are implemented on the database. The resulting 27 terabytes of data are public and can be accessed remotely through an interface based on a modern Web-services model. Users may write and execute analysis programs on their host computers, while the programs make subroutine-like calls (getFunctions) requesting desired variables (velocity and pressure, and their gradients) over the network. The architecture of the database and the initial built-in functionalities are described in a previous paper of Journal of Turbulence (Y. Li, E. Perlman, M. Wan, Y. Yang, R. Burns, C. Meneveau, R. Burns, S. Chen, A. Szalay, and G. Eyink, A public turbulence database cluster and applications to study Lagrangian evolution of velocity increments in turbulence, J. Turbul. 9 (2008), p. N31). In the present paper, further developments of the database system are described; mainly the newly developed getPosition function. Given an initial position, integration time-step, as well as an initial and end time, the getPosition function tracks arrays of fluid particles and returns particle locations at the end of the trajectory integration time. The getPosition function is tested by comparing with trajectories computed outside of the database. It is then applied to study the Lagrangian velocity structure functions as well as the tensor-based Lagrangian time correlation functions. The roles of pressure Hessian and viscous terms in the evolution of the symmetric and antisymmetric parts of the velocity gradient tensor are explored by comparing the time correlations with and without these terms. Besides the getPosition function, several other updates to the database are described such as a function to access the forcing term in the DNS, a new more efficient interpolation algorithm based on partial sums, and a new Matlab interface.

Rotating helical turbulence: three-dimensionalization or self-similarity in the small scales?

We present numerical evidence on how three-dimensionalization is recovered at small scale in rotating turbulence with helical forcing provided by a Beltrami flow. The relevant ranges (large-scale inverse cascade of energy, anisotropic and isotropic direct cascades of energy and helicity, dissipative) are each moderately resolved. These results stem from large direct numerical simulations on grids of either 15363 or 30723 points. In the latter case, the scale at which the inertial wave time and the eddy turn-over time are equal is found to be more than one order of magnitude larger than the dissipation scale. We also examine how the presence of such an intermediate scale could affect truncation due to the use of a helical spectral Large Eddy Simulation procedure which can allow for extending the analysis to a wider range of parameters. Finally, the self-similarity of the direct cascade of energy to small scales for rotating flows, observed recently in numerical simulations as well as in several laboratory experiments, will be discussed briefly for its scaling properties and its conformal invariance.

Preconditions and limitations of the postulate of scalar-dissipation–conductivity independence in a variable conductivity medium

Classical turbulent mixing paradigm--ingrained in scaling laws and closure models--is revisited in a variable-conductivity inhomogeneous medium. We perform direct numerical simulations to study the evolution of a passive scalar (temperature) field in a fluid with large conductivity gradients and investigate the behavior of scalar dissipation, conditional scalar dissipation, and velocity-to-scalar time scale ratio. Subject to the conditions of the investigation, it is found that these mixing characteristics become reasonably insensitive to conductivity after about one-third eddy turnover time. While the results support the classical paradigm, important preconditions and limitations are clearly identified.

On the Connection between Dissipation Enhancement in the Ocean Surface Layer and Langmuir Circulations

Abstract A mechanism for the enhancement of the viscous dissipation rate of turbulent kinetic energy (TKE) in the oceanic boundary layer (OBL) is proposed, based on insights gained from rapid-distortion theory (RDT). In this mechanism, which complements mechanisms purely based on wave breaking, preexisting TKE is amplified and subsequently dissipated by the joint action of a mean Eulerian wind-induced shear current and the Stokes drift of surface waves, the same elements thought to be responsible for the generation of Langmuir circulations. Assuming that the TKE dissipation rate ɛ saturates to its equilibrium value over a time of the order one eddy turnover time of the turbulence, a new scaling expression, dependent on the turbulent Langmuir number, is derived for ɛ. For reasonable values of the input parameters, the new expression predicts an increase of the dissipation rate near the surface by orders of magnitude compared with usual surface-layer scaling estimates, consistent with available OBL data. These results establish on firmer grounds a suspected connection between two central OBL phenomena: dissipation enhancement and Langmuir circulations.