Modelling the effects of horizontal and vertical shear in stratified turbulent flows

<p>Oceanic motions at scales larger than few tens of km are quasi-horizontal due to seawater stratification and Earth&#8217;s rotation and are characterized by quasi-two-dimensional turbulence. At scales around 300 km (in the mesoscale range), coherent vortices contain most of the kinetic energy in the ocean. At scales around 10 km (in the submesoscale range) the flow is populated by smaller eddies and filamentary structures associated with intense gradients (e.g. of temperature), which play an important role in both physical and biogeochemical budgets. Such small scales are found mainly in the weakly stratified mixed layer, lying on top of the more stratified thermocline. Submesoscale dynamics should strongly depend on the seasonal cycle and the associated mixed-layer instabilities. The latter are particularly relevant in winter and are responsible for the generation of energetic small scales that are not trapped at the surface, as those arising from mesoscale-driven processes, but extend down to the thermocline. The knowledge of the transport properties of oceanic flows at depth, which is essential to understand the coupling between surface and interior dynamics, however, is still limited.</p><p>By means of numerical simulations, we explore Lagrangian pair dispersion in turbulent flows from a quasi-geostrophic model consisting in two coupled fluid layers (representing the mixed layer and the thermocline) with different stratification. Such a model has been previously shown to give rise to both meso and submesoscale instabilities and subsequent turbulent dynamics that compare well with observations of wintertime submesoscale flows. We focus on the identification of different dispersion regimes and on the possibility to relate the characteristics of the spreading process at the surface and at depth, which is relevant to assess the possibility of inferring the dynamical features of deeper flows from the experimentally more accessible (e.g. by satellite altimetry) surface ones.</p><p>Using different statistical indicators, we find a clear transition of dispersion regime with depth, which is generic and can be related to the statistical features of the turbulent flows. The spreading process is local (namely, governed by eddies of the same size as the particle separation distance) at the surface. In the absence of a mixed layer it rapidly changes to nonlocal (meaning essentially driven by the largest eddies) at small depths, while in the opposite case this only occurs at larger depths, below the mixed layer. We then identify the origin of such behavior in the existence of fine-scale energetic structures due to mixed-layer instabilities. We further discuss the effect of vertical shear and address the properties of the relative motion of subsurface particles with respect to surface ones. In the absence of a mixed layer, the properties of the spreading process are found to rapidly decorrelate from those at the surface, but the relation between the surface and subsurface dispersion appears to be largely controlled by vertical shear. In the presence of mixed-layer instabilities, instead, the statistical properties of dispersion at the surface are found to be a good proxy for those in the whole mixed layer.</p>

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Relative dispersion in a model of stratified upper-ocean turbulence

10.5194/egusphere-egu2020-2671 ◽

2020 ◽

Author(s):

Stefano Berti ◽

Guillaume Lapeyre

Keyword(s):

Turbulent Flows ◽

Mixed Layer ◽

Fixed Time ◽

Separation Distance ◽

Vertical Shear ◽

Relative Dispersion ◽

Upper Ocean ◽

Dispersion Properties ◽

Dynamical Features ◽

Lagrangian Tracers

<div> <div> <div> <p>Turbulence in the upper ocean in the submesoscale range (scales smaller than the deformation radius) plays an important role for the heat exchange with the atmosphere and for oceanic biogeochemistry. Its dynamical features are thought to strongly depend on the seasonal cycle and the associated mixed-layer instabilities. The latter are particularly relevant in winter and are responsible for the fomation of energetic small scales that are not confined in a thin layer close to the surface, as those arising from mesoscale-driven processes, but extend over the whole depth of the mixed layer. The knowledge of the transport properties of oceanic flows at depth, however, is still limited, due to the complexity of performing measurements below the surface. Improving this knowledge is essential to understand how the surface dynamics couple with those of the ocean interior.</p> <p>By means of numerical simulations, here we explore the dispersion properties of turbulent flows in a quasi-geostrophic model system made of two coupled fluid layers (aimed to represent the mixed layer and the thermocline) with different stratification. Such a model has been previously shown to give rise to dynamics that compare well with observations of wintertime submesoscale flows. We examine the horizontal relative dispersion of Lagrangian tracers by means of both fixed-time and fixed-scale statistical indicators, at the surface and at depth, in the different dynamical regimes occurring in the presence, or not, of a mixed layer. The results indicate that, when mixed-layer instabilities are present, the dispersion regime is local (meaning governed by eddies of the same size as the particle separation distance) from the surface down to depths comparable with that of the interface with the thermocline. By contrasting this picture with what happens in the absence of a mixed layer, when dispersion quickly becomes nonlocal (i.e. dominated by the transport by the largest eddies) as a function of depth, we identify the origin of this behavior in the existence of fine-scale energetic structures due to mixed-layer instabilities. Finally, we discuss the effect of vertical shear on the tracer spreading process and address the correlation between the dispersion properties at the surface and in deeper layers, which is relevant to assess the possibility of inferring the dynamical features of deeper flows from the more accessible surface ones.</p> </div> </div> </div>

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The turbulent wake of a towed grid in a stratified fluid

Journal of Fluid Mechanics ◽

10.1017/jfm.2015.299 ◽

2015 ◽

Vol 775 ◽

pp. 149-177 ◽

Cited By ~ 6

Author(s):

X. Xiang ◽

T. J. Madison ◽

P. Sellappan ◽

G. R. Spedding

Keyword(s):

Density Gradient ◽

Turbulent Flows ◽

Initial Conditions ◽

Local Density ◽

Vertical Plane ◽

Stratified Fluid ◽

Vertical Shear ◽

Gradient Field ◽

Stratified Turbulence ◽

Background Density

In a stable background density gradient, initially turbulent flows eventually evolve into a state dominated by low-Froude-number dynamics and frequently also contain persistent pattern information. Much empirical evidence has been gathered on these latter stages, but less on how they first got that way, and how information on the turbulence generator may potentially be encoded into the flow in a robust and long-lasting fashion. Here an experiment is described that examines the initial stages of evolution in the vertical plane of a turbulent grid-generated wake in a stratified ambient. Refractive-index-matched fluids allow optically based measurement of early ($Nt<2$) stages of the flow, even when there are strong variations in the local density gradient field. Suitably averaged flow measures show the interplay between internal wave motions and Kelvin–Helmholtz-generated vortical modes. The vertical shear is dominant at the wake edge, and the decay of horizontal vorticity is observed to be independent of $\mathit{Fr}$. Stratified turbulence, originating from Kelvin–Helmholtz instabilities, develops up to non-dimensional time $Nt\approx 10$, and the scale separation between Ozmidov and Kolmogorov scales is independent of $\mathit{Fr}$ at higher $Nt$. The detailed measurements in the near wake, with independent variation of both Reynolds and Froude numbers, while limited to one particular case, are sufficient to show that the initial turbulence in a stratified fluid is neither three-dimensional nor universal. The search for appropriately generalizable initial conditions may be more involved than hoped for.

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Restricted equilibrium and the energy cascade in rotating and stratified flows

Journal of Fluid Mechanics ◽

10.1017/jfm.2014.540 ◽

2014 ◽

Vol 758 ◽

pp. 374-406 ◽

Cited By ~ 14

Author(s):

Corentin Herbert ◽

Annick Pouquet ◽

Raffaele Marino

Keyword(s):

Energy Spectrum ◽

Turbulent Flows ◽

Potential Vorticity ◽

Isotropic Turbulence ◽

Average Energy ◽

Negative Temperature ◽

Stratified Flows ◽

Vertical Shear ◽

Isotropic Energy ◽

Ideal System

AbstractMost turbulent flows appearing in nature (e.g. geophysical and astrophysical flows) are subjected to strong rotation and stratification. These effects break the symmetries of classical, homogenous isotropic turbulence. In doing so, they introduce a natural decomposition of phase space in terms of wave modes and potential vorticity modes. The appearance of a new time scale, associated with the propagation of waves, hinders the understanding of energy transfers across scales. For instance, it is difficult to predict a priori whether the energy cascades downscale as in homogeneous isotropic turbulence or upscale as expected from balanced dynamics. In this paper, we suggest a theoretical approach based on equilibrium statistical mechanics for the ideal system, inspired by the restricted partition function formalism introduced in metastability studies. We focus on the qualitative features of the inviscid system, taking into account either all the modes or just the slow modes. Specifically, we show that at absolute equilibrium, i.e. when all the modes are considered, no negative temperature states exist, and the isotropic energy spectrum is close to equipartition. By contrast, when the statistics is restricted to the contributions of the slow modes, we find that in the presence of rotation, there exists a regime of negative temperature featuring an infrared divergence in both the isotropic and the axisymmetric average energy spectrum, characteristic of an inverse cascade regime. Such regimes are not allowed for purely stratified flows, even in the restricted ensemble, because the slow manifold then partitions into modes that carry potential vorticity on the one hand, and hydrostatically balanced but vorticity-free modes, the so-called vertical shear horizontal flows, on the other hand, which forbid the appearance of negative temperatures.

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