Lagrangian pair dispersion in upper-ocean turbulent flows with mixed-layer instabilities

2021 ◽  
Author(s):  
Stefano Berti ◽  
Guillaume Lapeyre
Keyword(s):  
Turbulent Flows ◽  
Mixed Layer ◽  
Separation Distance ◽  
Vertical Shear ◽  
Spreading Process ◽  
Opposite Case ◽  
Dispersion Regime ◽  
Fluid Layers ◽  
Small Scales ◽  
Good Proxy

<p>Oceanic motions at scales larger than few tens of km are quasi-horizontal due to seawater stratification and Earth’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>

Relative dispersion in a model of stratified upper-ocean turbulence

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>

scholarly journals Intraseasonal Modulation of the Surface Cooling in the Gulf of Guinea

2013 ◽  
Vol 43 (2) ◽  
pp. 382-401 ◽  
Author(s):  
Julien Jouanno ◽  
Frédéric Marin ◽  
Yves du Penhoat ◽  
Jean-Marc Molines
Keyword(s):  
Mixed Layer ◽  
Gravity Waves ◽  
Heat Budget ◽  
Vertical Shear ◽  
Upper Ocean ◽  
Equatorial Waves ◽  
Gulf Of Guinea ◽  
The Core ◽  
Mixed Layer Heat Budget ◽  
Inertia Gravity Waves

Abstract A regional numerical model of the tropical Atlantic Ocean and observations are analyzed to investigate the intraseasonal fluctuations of the sea surface temperature at the equator in the Gulf of Guinea. Results indicate that the seasonal cooling in this region is significantly shaped by short-duration cooling events caused by wind-forced equatorial waves: mixed Rossby–gravity waves within the 12–20-day period band, inertia–gravity waves with periods below 11 days, and equatorially trapped Kelvin waves with periods between 25 and 40 days. In these different ranges of frequencies, it is shown that the wave-induced horizontal oscillations of the northern front of the mean cold tongue dominate the variations of mixed layer temperature near the equator. But the model mixed layer heat budget also shows that the equatorial waves make a significant contribution to the mixed layer heat budget through modulation of the turbulent cooling, especially above the core of the Equatorial Undercurrent (EUC). The turbulent cooling variability is found to be mainly controlled by the intraseasonal modulation of the vertical shear in the upper ocean. This mechanism is maximum during periods of seasonal cooling, especially in boreal summer, when the surface South Equatorial Current is strongest and between 2°S and the equator, where the presence of the EUC provides a background vertical shear in the upper ocean. It applies for the three types of intraseasonal waves. Inertia–gravity waves also modulate the turbulent heat flux at the equator through vertical displacement of the core of the EUC in response to equatorial divergence and convergence.

Kolmogorov’s contributions to the physical and geometrical understanding of small-scale turbulence and recent developments

1991 ◽  
Vol 434 (1890) ◽  
pp. 183-210 ◽  
Keyword(s):  
Turbulent Flows ◽  
Large Scale ◽  
Inertial Range ◽  
Small Scale ◽  
Small Scales ◽  
Recent Developments ◽  
Self Similar ◽  
Scale Turbulence ◽  
High Reynolds ◽  
Non Gaussian

This paper reviews how Kolmogorov postulated for the first time the existence of a steady statistical state for small-scale turbulence, and its defining parameters of dissipation rate and kinematic viscosity. Thence he made quantitative predictions of the statistics by extending previous methods of dimensional scaling to multiscale random processes. We present theoretical arguments and experimental evidence to indicate when the small-scale motions might tend to a universal form (paradoxically not necessarily in uniform flows when the large scales are gaussian and isotropic), and discuss the implications for the kinematics and dynamics of the fact that there must be singularities in the velocity field associated with the - 5/3 inertial range spectrum. These may be particular forms of eddy or ‘eigenstructure’ such as spiral vortices, which may not be unique to turbulent flows. Also, they tend to lead to the notable spiral contours of scalars in turbulence, whose self-similar structure enables the ‘box-counting’ technique to be used to measure the ‘capacity’ D K of the contours themselves or of their intersections with lines, D' K . Although the capacity, a term invented by Kolmogorov (and studied thoroughly by Kolmogorov & Tikhomirov), is like the exponent 2 p of a spectrum in being a measure of the distribution of length scales ( D' K being related to 2 p in the limit of very high Reynolds numbers), the capacity is also different in that experimentally it can be evaluated at local regions within a flow and at lower values of the Reynolds number. Thus Kolmogorov & Tikhomirov provide the basis for a more widely applicable measure of the self-similar structure of turbulence. Finally, we also review how Kolmogorov’s concept of the universal spatial structure of the small scales, together with appropriate additional physical hypotheses, enables other aspects of turbulence to be understood at these scales; in particular the general forms of the temporal statistics such as the high-frequency (inertial range) spectra in eulerian and lagrangian frames of reference, and the perturbations to the small scales caused by non-isotropic, non-gaussian and inhomogeneous large-scale motions.

Wave-vortex dynamics in rotating shallow water

1989 ◽  
Vol 206 ◽  
pp. 433-462 ◽  
Author(s):  
Marie Farge ◽  
Robert Sadourny
Keyword(s):  
Shallow Water ◽  
Turbulent Flows ◽  
Gravitational Energy ◽  
Energy Cascade ◽  
Adjustment Process ◽  
Coherent Vortices ◽  
Small Scales ◽  
Direct Energy ◽  
Incompressibility Constraint ◽  
Rotating Shallow Water

We investigate how two-dimensional turbulence is modified when the incompressibility constraint is removed, by numerically integrating the full Saint-Venant (shallow-water) equations. In the case of small geopotential fluctuations considered here, we find no energy exchange between the inertio-gravitational and the potentio-vortical components of the flow. At small scales, the potentio-vortical component behaves as if the flow were incompressible, while we observe an intense direct energy cascade within the inertio-gravitational component. At large scales, the reverse potentio-vortical energy cascade is reduced when the level of inertio-gravitational energy is high. Looking at the effect of rotation, we find that a fast rotation rate tends to inhibit all three cascades. In particular, the inhibition of the inertio-gravitational energy cascade towards small scales implies that the geostrophic adjustment process is hindered by an increase of rotation. Concerning the structure of the coherent vortices emerging out of these decaying turbulent flows, we observe that the smallest scales are concentrated inside the vortex cores and not on their periphery.

Spectral analysis of energy transfer in turbulent flows laden with heated particles

2017 ◽  
Vol 813 ◽  
pp. 1156-1175 ◽  
Author(s):  
H. Pouransari ◽  
H. Kolla ◽  
J. H. Chen ◽  
A. Mani
Keyword(s):  
Energy Transfer ◽  
Turbulent Flows ◽  
Turbulent Combustion ◽  
Stokes Number ◽  
Turbulence Modification ◽  
Wide Range ◽  
Small Scales ◽  
Divergence Free ◽  
Particle Heating ◽  
Transfer Term

In this study we consider particle-laden turbulent flows with significant heat transfer between the two phases due to sustained heating of the particle phase. The sustained heat source can be due to particle heating via an external radiation source as in the particle-based solar receivers or an exothermic reaction in the particles. Our objective is to investigate the effects of fluid heating by a dispersed phase on the turbulence evolution. An important feature in such settings is the preferential clustering phenomenon which is responsible for non-uniform distribution of particles in the fluid medium. Particularly, when the ratio of particle inertial relaxation time to the turbulence time scale, namely the Stokes number, is of order unity, particle clustering is maximized, leading to thin regions of heat source similar to the flames in turbulent combustion. However, unlike turbulent combustion, a particle-laden system involves a wide range of clustering scales that is mainly controlled by particle Stokes number. To study these effects, we considered a decaying homogeneous isotropic turbulence laden with heated particles over a wide range of Stokes numbers. Using a low-Mach-number formulation for the fluid energy equation and a Lagrangian framework for particle tracking, we performed numerical simulations of this coupled system. We then applied a high-fidelity framework to perform spectral analysis of kinetic energy in a variable-density fluid. Our results indicate that particle heating can considerably influence the turbulence cascade. We show that the pressure-dilatation term introduces turbulent kinetic energy at a range of scales consistent with the scales observed in particle clusters. This energy is then transferred to high wavenumbers via the energy transfer term. For low and moderate levels of particle heating intensity, quantified by a parameter $\unicode[STIX]{x1D6FC}$ defined as the ratio of eddy time to mean temperature increase time, turbulence modification occurs primarily in the dilatational modes of the velocity field. However, as the heating intensity is increased, the energy transfer term converts energy from dilatational modes to divergence-free modes. Interestingly, as the heating intensity is increased, the net modification of turbulence by heating is observed dominantly in divergence-free modes; the portion of turbulence modification in dilatational modes diminishes with higher heating. Moreover, we show that modification of divergence-free modes is more pronounced at intermediate Stokes numbers corresponding to the maximum particle clustering. We also present the influence of heating intensity on the energy transfer term itself. This term crosses over from negative to positive values beyond a threshold wavenumber, showing the cascade of energy from large scales to small scales. The threshold is shown to shift to higher wavenumbers with increasing heating, indicating a growth in the total energy transfer from large scales to small scales. The fundamental energy transfer analysis presented in this paper provides insightful guidelines for subgrid-scale modelling and large-eddy simulation of heated particle-laden turbulence.

The turbulent wake of a towed grid in a stratified fluid

2015 ◽  
Vol 775 ◽  
pp. 149-177 ◽  
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.

scholarly journals Turbulence via information field dynamics

2015 ◽  
Vol 11 (A29B) ◽  
pp. 730-730
Author(s):  
Torsten A. Enßlin
Keyword(s):  
Turbulent Flows ◽  
Theoretical Framework ◽  
Statistical Information ◽  
Statistical Properties ◽  
Length Scales ◽  
Scale Free ◽  
Statistical Knowledge ◽  
Flow Fluctuations ◽  
Small Scales

AbstractTurbulent flows exhibit scale-free regimes, for which information on the statistical properties of the dynamics exists for many length-scales. The simulation of turbulent systems can benefit from the inclusion of such information on sub-grid process. How can statistical information about the flow on small scales be optimally incorporated into simulation schemes? Information field dynamics (IFD) is a novel information theoretical framework to design schemes that exploit such statistical knowledge on sub-grid flow fluctuations.

Sign in / Sign up

Export Citation Format

Share Document