Decaying grid turbulence in a rotating stratified fluid

arXiv (Cornell University), 2009

The effect of a background rotation on the decay of homogeneous turbulence produced by a grid is experimentally investigated. Experiments have been performed in a channel mounted in the large-scale 'Coriolis' rotating platform, and measurements have been carried out in the planes normal and parallel to the rotation axis using particle image velocimetry. After a short period of about 0.4 tank rotation where the energy decays as t −6/5 , as in classical isotropic turbulence, the energy follows a shallower decay law compatible with t −3/5 , as dimensionally expected for energy transfers governed by the linear timescale Ω −1. The crossover occurs at a Rossby number Ro ≃ 0.25, without noticeable dependence with the grid Rossby number. After this transition, anisotropy develops in the form of vertical layers where the initial vertical velocity remains trapped. These layers of nearly constant vertical velocity become thinner as they are advected and stretched by the large-scale horizontal flow, producing significant horizontal gradient of vertical velocity which eventually become unstable. After the Ro ≃ 0.25 transition, the vertical vorticity field first develops a cyclone-anticyclone asymmetry, reproducing the growth law of the vorticity skewness, S ω (t) ≃ (Ωt) 0.7 , reported by Morize, Moisy & Rabaud [Phys. Fluids 17 (9), 095105 (2005)]. At larger time, however, the vorticity skewness decreases and eventually returns to zero. The present results indicate that the shear instability of the vertical layers contribute significantly to the re-symmetrisation of the vertical vorticity at large time, by re-injecting vorticity fluctuations of random sign at small scales. These results emphasize the importance of the initial conditions in the decay of rotating turbulence.

Journal of Fluid Mechanics, 2005

Grid turbulence experiments have been carried out in a stably stratified fluid at moderately large Reynolds numbers (160 based on the Taylor microscale). A scanning particle image velocimetry technique is used to provide time-resolved velocity fields in a relatively large volume. For late times, in the low-Froude-number regime, the flow consists of quasi-horizontal motion in a sea of weak internal gravity waves. Here the dynamics of the flow is found to be independent of the ambient stratification. Fundamental differences with two-dimensional turbulence, due to the strong vertical shearing of horizontal velocity, are observed. In this regime, a self-similar scaling law for the energy decay and the length-scale evolution is observed. This behaviour reflects a process of adjustment of the eddy aspect ratio based on a balance between the horizontal advective motion which tends to vertically decorrelate the flow and the dissipation due to strong vertical shear. The characteristic vertical size of the eddies grows according to a diffusion law and is found to be independent of the turbulence generation. The organization of the flow into horizontal layers of eddies separated by intense shear leads to a strong anisotropy of the dissipation: this has been checked by direct measurement of the different tensorial components of the viscous dissipation.

Atmospheric and oceanic flows are strongly affected by rotation and stratification. Rotation is exerted through Coriolis forces which mainly act in horizontal planes whereas stratification largely affects the motion along the vertical direction through buoyancy forces, the latters related to the vertical variation of the fluid density. Aiming at a better understanding of atmospheric and oceanic processes, in this thesis the properties of turbulence in rotating and stably stratified flows are studied by means of numerical simulations, with and without the presence of solid walls. A new code is developed in order to carry out high-resolution numerical simulations of geostrophic turbulence forced at large scales. The code was heavily parallelized with MPI (Message Passing Interface) in order to be run on massively parallel computers. The main problem which has been investigated is how the turbulent cascade is affected by the presence of strong but finite rotation and stratification. As opposed to the early theories in the field of geostrophic turbulence, we show that there is a forward energy cascade which is initiated at large scales. The contribution of this process to the general dynamic is secondary at large scales but becomes dominant at smaller scales where leads to a shallowing of the energy spectrum. Despite the idealized setup of the simulations, two-point statistics show remarkable agreement with measurements in the atmosphere, suggesting that this process may be an important mechanism for energy transfer in the atmosphere. The effect of stratification in wall-bounded turbulence is investigated by means of direct numerical simulations of open-channel flows. An existing fullchannel code was modified in order to optimize the grid in the vertical direction and avoid the clustering of grid points at the upper boundary, where the solid wall is replaced by a free-shear condition. The stable stratification which results from a cooling applied at the solid wall largely affects the outer structures of the boundary layer, whereas the near-wall structures appear to be mostly unchanged. The effect of gravity waves is also studied, and a new decomposition is introduced in order to separate the gravity wave field from the turbulent field.

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.

Atmospheric and Oceanographic Sciences Library, 2014

This book presents an extensive analysis of the dynamics of discrete and distributed baroclinic vortices in a multi-layer fluid that characterizes the main features of the large and mesoscales dynamics of the atmosphere and the ocean. It widely covers the case of hetonic situations as well as the case of intrathermocline vortices that are familiar in oceanographic and of recognized importance for heat and mass transfers. Extensive typology of such baroclinic eddies is made and analysed with the help of theoretical development and numerical computations. As a whole it gives an overview and synthesis of all the many situations that can be encountered based on the long history of the theory of vortex motion and on many new situations. It gives a renewed insight on the extraordinary richness of vortex dynamics and open the way for new theoretical, observational and experimental advances. This volume is of interest to experts in physical oceanography, meteorology, hydrodynamics, dynamic systems, involved in theoretical, experimental and applied research and lecturers, post-graduate students, and students in these fields.

Dynamics of Atmospheres and Oceans, 1996

Full field digital particle image velocimetry (DPIV) measurements of strongly stratified grid turbulence have been carried out for long times (up to Nt = 1000). Quasi-2D vortices were formed that were separated vertically by strong horizontal vortex sheets. Dissipation scales were resolved and the relative dissipation fractions in the horizontal and vertical planes were determined. A simple vortex model, involving a dense packing of discus-shaped structures connected by vortex lines that alternate between horizontal and vertical orientation, is shown to be consistent with both the observed velocity and vorticity fields, and the evolution of the measured length scales in orthogonal planes.

Dynamics of Atmospheres and Oceans, 1997

A series of experiments is described in which a turbulent patch is generated locally by an oscillating grid positioned at one end and mid-depth of a rotating channel filled initially with a linearly-stratified fluid. Measurements have been made of vertical density profiles through the patch both during sustained oscillations and followitg cessation of grid forcing. Temporal variations in patch size and structure, Thorpe scales, mixedness parameter and available potential energy are deduced from these measurements, and the effects thereon of varying the background rotation rate, initial buoyancy frequency and grid action are investigated. For the growth phase of the patch, previous results obtained by other workers are confirmed and extended. Because the rapid turbulent motions implied a large Rossby number, rotation was not important during this phase. During the decay phase, rotational effects are shown to become important, and the presence of rotation is found to retard the decay of both the mixedness and the Thorpe scales of the density overturns within the patch. The work is novel in that measurements of the patch parameters listed above have not previously been carried out in the presence of rotation. The results are relevant to studies of such patches that have been observed in the ocean and atmosphere. c fJ J J J J

Journal of Turbulence, 2005

Nonlinear approaches such as direct numerical simulations (DNS) yield a characteristic structuring in homogeneous turbulence as a result of modified dynamics under the effect of rotation and stable stratification. The structures are elongated for dominant rotation or flat when stratification dominates. Nonlinearity is essential for constructing these anisotropic Eulerian features, which we quantify by single and two-point second-order statistics. Linear approaches such as rapid distorsion theory (RDT) and kinematic simulations (KS) do not reproduce these effects at all. However, when looking at Lagrangian statistics, both linear and nonlinear models seem to yield very similar anisotropic trends. In order to investigate this paradox, we consider statistically homogeneous turbulence with vertical stable stratification characterized by the Brunt-Väisälä frequency N and vertical system rotation with frequency in the Boussinesq system of equations. For different values of the ratio 2 /N , we compare Eulerian and Lagrangian statistics. The detailed dynamics of energy is studied by splitting the velocity in toroidal and poloidal modes, which we put in relation with the wave/vortex linear decomposition. From DNS, the results for dominant stratification show a large disequilibrium of anisotropy between the toroidal and poloidal parts. For dominant rotation, angular spectra show an equidistribution of energy between poloidal and toroidal parts, with non-isotropic angular distribution of the energy density down to the smallest scales. Regarding Lagrangian statistics, DNS results are compared with two linear models based on RDT and KS, respectively. The linear models reproduce extremely well the oscillations and confinement of vertical one-point dispersion when stratification is present. Horizontal diffusion laws compare well in a qualitative way. However, quantitative differences can be detected.

Dynamics of Atmospheres and Oceans, 1996

Stably stratified rotating turbulence is numerically investigated both with energy injection at small scales and in a freely decaying situation. To discriminate between the turbulent geostrophic part of the motion and the component associated with the inertial-gravity waves two decompositions are used. The first is based upon the fact that the wave field has no potential vorticity, and the second consists of a normal-mode decomposition. Both in the forced and freely decaying cases, the regime of small Froude and Rossby numbers is characterized by an inverse cascade of geostrophic energy towards the large scales whereas the wave energy propagates towards the dissipative scales. In the forced case, the inverse cascade corresponds to a well-defined k-5/3 spectral range for both the kinetic and available potential energy spectra. The applications to the observed mesoscale atmospheric spectrum are discussed.

Journal of Fluid Mechanics, 2010

The effect of a background rotation on the decay of grid-generated turbulence is investigated from experiments using the large-scale ‘Coriolis’ rotating platform. A first transition occurs at 0.4 tank rotation (instantaneous Rossby number Ro ≃ 0.25), characterized by a t−6/5 → t−3/5 transition of the energy-decay law. After this transition, anisotropy develops in the form of vertical layers, where the initial vertical velocity fluctuations remain trapped. The vertical vorticity field develops a cyclone–anticyclone asymmetry, reproducing the growth law of the vorticity skewness, Sω(t) ≃ (Ωt)0.7, reported by Morize, Moisy & Rabaud (Phys. Fluids, vol. 17 (9), 2005, 095105). A second transition is observed at larger time, characterized by a return to vorticity symmetry. In this regime, the layers of nearly constant vertical velocity become thinner as they are advected and stretched by the large-scale horizontal flow, and eventually become unstable. The present results indicate that the ...