Numerical investigation of rotating and stratified turbulence

This Letter presents results of the first direct numerical simulations of rotating Rayleigh-Bénard convection in the so-called geostrophic regime, (hence very small Ekman numbers O(10 −7) and high Rayleigh numbers Ra = 10 10 and 5 • 10 10), employing the full Navier-Stokes equations. In the geostrophic regime the criteria of very strong rotation and large supercriticality are met simultaneously, which is true for many geophysical and astrophysical flows. Until now, numerical approaches of this regime have been based on reduced versions of the Navier-Stokes equations (cf. Sprague et al. J. Fluid Mech., 551, 141 (2006)), omitting the effect of the viscous (Ekman) boundary layers. By using different velocity boundary conditions at the plates, we study the effect of these Ekman layers. We find that the formation of large-scale structures (Rubio et al. (Phys. Rev. Lett. 112 (2014)), which indicates the presence of an inverse energy cascade, does not take place when the Ekman layers are present (i.e., for no-slip plates). For very strong background rotation Ekman pumping is an important source of fluctuations. This causes the heat transfer to be larger for no-slip boundary conditions as compared to stress-free boundary conditions.

2013

Although turbulence has been studied for more than five hundred years, a thorough understanding of turbulent flows is still missing. Nowadays computing power can offer an alternative tool, besides ...

Density stratification has a strong impact on turbulence in geophysical flows. Stratification changes the spatial turbulence spectrum and the energy transport and conversion within the spectrum. We analyze these effects based on a series of direct numerical simulations (DNS) of stratified turbulence. To facilitate simulations of real-world problems, which are usually beyond the reach of DNS, we propose a subgrid-scale turbulence model for large eddy simulations of stratified flows based on the Adaptive Local Deconvolution Method (ALDM). Flow spectra and integral quantities predicted by ALDM are in excellent agreement with direct numerical simulation. ALDM automatically adapts to strongly anisotropic turbulence and is thus a suitable tool for studying turbulent flow phenomena in atmosphere and ocean.

ERCOFTAC Series, 2011

Physics of Fluids, 2011

Physics of Fluids, 2019

This paper investigates the processes by which stable boundary layers are formed through strong surface cooling imposed on neutrally stratified wall-bounded turbulence using high-resolution direct numerical simulation at a moderate Reynolds number. The adjustment of the flow to the imposed strong surface cooling is investigated. We further focus on a strongly stable case where turbulence partially collapses. We show that, due to a significant reduction in turbulence production, turbulence becomes patchy, with a band of turbulence coexisting with quiet regions. The nature of the quiet regions, which are often characterized as laminar, is investigated and shown to be consistent with viscously coupled stratified turbulence. The one-dimensional longitudinal streamwise velocity spectrum exhibits k −5 x and k −3 x behavior in the buffer and logarithmic layers, respectively, adjacent to an active region of three-dimensional turbulence with a k −5/3 x spectrum. Scenarios for turbulence recovery from such a patchy state are also discussed. We show that the presence of outer layer turbulence above z + ≈ 300 is a key requirement for recovery. For higher values of stratification, it is shown that inner layer turbulence is damped entirely and outer layer turbulence is damped subsequently.

Physics of Fluids, 2015

An experimental investigation of the flow over two-and three-dimensional large-scale wavy walls was performed using high-resolution planar particle image velocimetry in a refractive-index-matching (RIM) channel. The 2D wall is described by a sinusoidal wave in the streamwise direction with amplitude to wavelength ratio a/λ x = 0.05. The 3D wall is defined with an additional wave superimposed on the 2D wall in the spanwise direction with a/λ y = 0.1. The flow over these walls was characterized at Reynolds numbers of 4000 and 40 000, based on the bulk velocity and the channel half height. Flow measurements were performed in a wall-normal plane for the two cases and in wall-parallel planes at three heights for the 3D wavy wall. Instantaneous velocity fields and time-averaged turbulence quantities reveal strong coupling between large-scale topography and the turbulence dynamics near the wall. Turbulence statistics show the presence of a well-structured shear layer that enhances the turbulence for the 2D wavy wall, whereas the 3D wall exhibits different flow dynamics and significantly lower turbulence levels. It is shown that the 3D surface limits the dynamics of the spanwise turbulent vortical structures, leading to reduced turbulence production and turbulent stresses and, consequently, lower average drag (wall shear stress). The likelihood of recirculation bubbles, levels and spatial distribution of turbulence, and rate of the turbulent kinetic energy production are shown to be severely affected when a single spanwise mode is superimposed on the 2D sinusoidal wall. Differences of one and two order of magnitudes are found in the turbulence levels and Reynolds shear stress at the low Reynolds number for the 2D and 3D cases. These results highlight the sensitivity of the flow to large-scale topographic modulations; in particular the levels and production of turbulent kinetic energy as well as the wall shear stress.

Physics of Fluids, 2014

Theoretical and Computational Fluid Dynamics, 2011

A Finite Volume-based large-eddy simulation method is proposed along with a suitable extension of the dynamic modelling procedure that takes into account for the integral formulation of the governing filtered equations. Discussion about the misleading interpretation of FV in some literature is addressed. Then, the classical Germano identity is congruently rewritten in such a way that the determination of the modelling parameters does not require any arbitrary averaging procedure and thus retains a fully local character. The numerical modelling of stratified turbulence is the specific problem considered in this study, as an archetypal of simple geophysical flows. The original scaling formulation of the dynamic sub-grid scale model proposed by Wong and Lilly (Phys. Fluids 6(6), 1994) is suitably extended to the present integral formulation. This approach is preferred with respect to traditional ones since the eddy coefficients can be independently computed by avoiding the addition of unjustified buoyancy production terms in the constitutive equations. Simple scaling arguments allow us not to use the equilibrium hypothesis according to which the dissipation rate should equal the sub-grid scale energy production. A careful a priori analysis of the relevance of the test filter shape as well as the filter-to-grid ratio is reported. Large-eddy simulation results are a posteriori compared with a reference pseudo-spectral direct numerical solution that is suitably post-filtered in order to have a meaningful comparison. In particular, the spectral distribution of kinetic and thermal energy as well as the viscosity and diffusivity sub-grid scale profiles are illustrated. The good performances of the proposed method, in terms of both evolutions of global quantities and statistics, are very promising for the future development and application of the method. supposed to be effective by means of an explicit/implicit filtering operation. Different SGS models for LES have been developed during the last two decades, i.e. the eddy-viscosity, scale-similarity and mixed models, as well as the more recent approximate deconvolution and Lagrangian models, . Moreover, the dynamic procedure proposed in allows for a wider feasibility as it can be applied to all modelling procedures, but it remains generally developed under the same equilibrium hypothesis of the Boussinesq sub-grid viscosity approach.

The effect of grid topology and resolution is studied for decaying, homogenous isotropic turbulence using unstruc-tured grids. The grid topology is examined via an ap-proach which includes grids of structured-like quality (or-dered hexahedra) and also grids which consist entirely of random tetrahedra. The grid resolution is varied to include three levels for each topology. Decaying turbulence is cho-sen for its well-documented behavior and ease for examin-ing statistical quantities. It is expected that not all turbu-lence models will behave the same on all grids. To limit such variability, Delayed Detached Eddy Simulations are considered exclusively. Metrics of merit include the en-ergy spectra measured at two different times, the decay of the resolved turbulent kinetic energy, time history of the skewness and kurtosis of the velocity gradients, and the evolution of the transverse Taylor microscale. Data are compared to available experiments. The goal of this work is to provide guid...

Boundary-Layer Meteorology, 2009

We advance our prior energy-and flux-budget (EFB) turbulence closure model for the stably stratified atmospheric flows and extend it accounting for additional vertical flux of momentum and additional productions of turbulent kinetic energy (TKE), turbulent potential energy (TPE) and turbulent flux of potential temperature due to large-scale internal gravity waves (IGW). For the stationary, homogeneous regime, the first version of the EFB model disregarding large-scale IGW yielded universal dependencies of the flux Richardson number, turbulent Prandtl number, energy ratios, and normalised vertical fluxes of momentum and heat on the gradient Richardson number, Ri. Due to the large-scale IGW, these dependencies lose their universality. The maximal value of the flux Richardson number (universal constant  0.2-0.25 in the no-IGW regime) becomes strongly variable. In the vertically homogeneous stratification, it increases with increasing wave energy and can even exceed 1. In the heterogeneous stratification, when IGW propagate towards stronger stratification, the maximal flux Richardson number decreases with increasing wave energy, reaches zero and then becomes negative. In other words, the vertical flux of potential temperature becomes counter-gradient. IGW also reduce anisotropy of turbulence: in contrast to the mean wind shear, which generates only horizontal TKE, IGW generate both horizontal and vertical TKE. IGW also increase the share of TPE in the turbulent total energy (TTE = TKE + TPE). A well-known effect of IGW is their direct contribution to the vertical transport of momentum. Depending on the direction (downward or upward), IGW either strengthen or weaken the total vertical flux of momentum. Predictions from the proposed model are consistent with available data from atmospheric and laboratory experiments, direct numerical simulations and large-eddy simulations.

Physics of Fluids, 2005

Large eddy simulation has been used to study flow in an open channel with stable stratification imposed at the free surface by a constant heat flux and an adiabatic bottom wall. This leads to a stable pycnocline overlying a well-mixed turbulent region near the bottom wall. The results are contrasted with studies in which the bottom heat flux is nonzero, a difference analogous to that between oceanic and atmospheric boundary layers. Increasing the friction Richardson number, a measure of the relative importance of the imposed surface stratification with respect to wallgenerated turbulence, leads to a stronger, thicker pycnocline which eventually limits the impact of wall-generated turbulence on the free surface. Increasing stratification also leads to an increase in the pressure-driven mean streamwise velocity and a concomitant decrease in the skin friction coefficient, which is, however, smaller than in the previous channel flow studies where the bottom buoyancy flux was nonzero. It is found that the turbulence in any given region of the flow can be classified into three regimes (unstratified, buoyancy-affected, and buoyancy-dominated) based on the magnitude of the Ozmidov length scale relative to a vertical length characterizing the large scales of turbulence and to the Kolmogorov scale. Since stratification does not strongly influence the near-wall turbulent production in the present configuration, the behavior of the buoyancy flux, turbulent Prandtl number, and mixing efficiency is qualitatively different from that seen in stratified shear layers and in channel flow with fixed temperature walls, and, furthermore, collapse of quantities as a function of gradient Richardson number is not observed. The vertical Froude number is a better measure of stratified turbulence in the upper portion of the channel where buoyancy, by providing a potential energy barrier, primarily affects the transport of turbulent patches generated at the bottom wall. The characteristics of free-surface turbulence including the kinetic energy budget and pressure-strain correlations are examined and found to depend strongly on the surface stratification. (Large eddy simulation has been used to study flow in an open channel with stable stratification imposed at the free surface by a constant heat flux and an adiabatic bottom wall. This leads to a stable pycnocline overlying a well-mixed turbulent region near the bottom wall. The results are contrasted with studies in which the bottom heat flux is nonzero, a difference analogous to that between oceanic and atmospheric boundary layers. Increasing the friction Richardson number, a measure of the relative importance of the imposed surface stratification with respect to wall-generated turbulence, leads to a stronger, thicker pycnocline which eventually limits the impact of wall-generated turbulence on the free surface. Increasing stratification also leads to an increase in the pressure-driven mean streamwise velocity and a concomitant decrease in the skin friction coefficient, which is, however, smaller than in the previous channel flow studies where the bottom buoyancy flux was nonzero. It is found that the turbulence in any given region of the flow can be classified into three regimes ͑unstratified, buoyancy-affected, and buoyancy-dominated͒ based on the magnitude of the Ozmidov length scale relative to a vertical length characterizing the large scales of turbulence and to the Kolmogorov scale. Since stratification does not strongly influence the near-wall turbulent production in the present configuration, the behavior of the buoyancy flux, turbulent Prandtl number, and mixing efficiency is qualitatively different from that seen in stratified shear layers and in channel flow with fixed temperature walls, and, furthermore, collapse of quantities as a function of gradient Richardson number is not observed. The vertical Froude number is a better measure of stratified turbulence in the upper portion of the channel where buoyancy, by providing a potential energy barrier, primarily affects the transport of turbulent patches generated at the bottom wall. The characteristics of free-surface turbulence including the kinetic energy budget and pressure-strain correlations are examined and found to depend strongly on the surface stratification.

This work investigates the structure and the dacay of turbulence in stratified and rotating flows. The role of vorticity in 2D flows produces an inverse cascade towards the larger scales. When Stratification and/or Rotation act, the spectra of the process tends towards a E(k) = k^(-3) spectral slope as in the enstrophy cascade. The PIV experimental velocity and vorticity measurements show that the decay law for the number of vortices does not follow the 2D conditions except in the limit of ver high Richardson number and very low Rossby number. Stratification and Rotation act in a highly non-linear fashion modifying the number of vortices by radiation of energy by internal and inertial waves.

Journal of Fluid Mechanics, 2021

Continuously forced, stratified shear flows occur in many geophysical systems, including flow over sills, through fjords and at the mouths of rivers and estuaries. These continuously forced shear flows can be unstable and drive turbulence, which can enhance the rate of mixing. In this study, we analyse three-dimensional direct numerical simulations of an idealized stratified shear flow that is continuously forced by weakly relaxing both the buoyancy and streamwise velocity towards prescribed mean profiles. We explore a range of large and small Richardson numbers, for constant Reynolds and Prandtl numbers (Re = 4000 and Pr = 1). After a turbulent steady state develops, three regimes are observed: (i) a weakly stratified, overturning regime, (ii) a strongly stratified, scouring regime and (iii) an intermediately stratified, intermittent regime. The overturning regime exhibits partially formed overturning billows that break down into turbulence and broaden the velocity and buoyancy interfaces. Conversely, the scouring regime exhibits internal gravity waves propagating along the strongly stratified buoyancy interface, while turbulence on either side of the buoyancy interface reinforces the stratification. The intermediate regime quasi-periodically alternates between behaviours associated with the overturning and scouring regimes. For each case, we quantify an appropriate measure of the efficiency of mixing and examine its dependence on relevant parameters including appropriate definitions of the buoyancy Reynolds number, gradient Richardson number and horizontal Froude numbers. Using a framework involving sorted buoyancy coordinates as introduced by Nakamura (J.