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.

Numerical simulations of freely evolving turbulence in stably stratified fluids

1989 ◽  
Vol 202 ◽  
pp. 117-148 ◽  
Author(s):  
Olivier Métais ◽  
Jackson R. Herring
Keyword(s):  
Initial Data ◽  
Numerical Simulations ◽  
Initial Conditions ◽  
Vertical Shear ◽  
Temperature Structure ◽  
Two Dimensional ◽  
Stratified Turbulence ◽  
Statistical Parameters ◽  
Frequency Spectra ◽  
Thorpe Scale

Results of direct numerical simulations of stably stratified, freely evolving, homogeneous turbulence are presented. An examination of initial data designed to give insight into laboratory flows suggests that the numerical simulations have a satisfactory degree of realism, insofar as statistical parameters such as total energy and length scales are concerned. The motion is decomposed into a stratified turbulence (vortical) component and a wave component. For initial-value problems similar to laboratory studies of stratified flows, the vortical component decays at a rate virtually identical to that of the non-buoyant case up to t = 6N−1 (N is the Brunt-Väisälä frequency). The decay rate decreases after this time, suggesting a kind of turbulence ‘collapse’. The temperature structure that emerges clearly shows the development of the collapse stage of the flow, which is also diagnosed by the behaviour of parameters such as the Thorpe scale.We next examine the very small-Froude-number regime in order to understand possible universal aspects of the flow. An examination of various initial conditions with different proportions of stratified and wave components indicates a lack of universality. For initial data containing only vortical motion (motions derived from the vertical vorticity field), the vortical field tends to dominate, in subsequent evolution, at strong stratification. However, contrary to two-dimensional turbulence, the flow is more strongly dissipative than two-dimensional flows due to the frictional effect associated with layering. Other quantities examined are frequency spectra, and the probability distribution for vertical shear. The frequency spectra exhibit some features in common with spectra extracted from oceanographic data.

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

&lt;p&gt;Oceanic motions at scales larger than few tens of km are quasi-horizontal due to seawater stratification and Earth&amp;#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.&lt;/p&gt;&lt;p&gt;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.&lt;/p&gt;&lt;p&gt;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.&lt;/p&gt;

scholarly journals Waves and vortices in the inverse cascade regime of stratified turbulence with or without rotation

2016 ◽  
Vol 806 ◽  
pp. 165-204 ◽  
Author(s):  
Corentin Herbert ◽  
Raffaele Marino ◽  
Duane Rosenberg ◽  
Annick Pouquet
Keyword(s):  
Reynolds Number ◽  
Numerical Simulations ◽  
Direct Numerical Simulations ◽  
Vertical Shear ◽  
Energy Spectra ◽  
Stratified Turbulence ◽  
Viscous Effects ◽  
Inverse Cascade ◽  
Main Effects ◽  
The Waves

We study the partition of energy between waves and vortices in stratified turbulence, with or without rotation, for a variety of parameters, focusing on the behaviour of the waves and vortices in the inverse cascade of energy towards the large scales. To this end, we use direct numerical simulations in a cubic box at a Reynolds number $Re\approx 1000$, with the ratio between the Brunt–Väisälä frequency $N$ and the inertial frequency $f$ varying from $1/4$ to 20, together with a purely stratified run. The Froude number, measuring the strength of the stratification, varies within the range $0.02\leqslant Fr\leqslant 0.32$. We find that the inverse cascade is dominated by the slow quasi-geostrophic modes. Their energy spectra and fluxes exhibit characteristics of an inverse cascade, even though their energy is not conserved. Surprisingly, the slow vortices still dominate when the ratio $N/f$ increases, also in the stratified case, although less and less so. However, when $N/f$ increases, the inverse cascade of the slow modes becomes weaker and weaker, and it vanishes in the purely stratified case. We discuss how the disappearance of the inverse cascade of energy with increasing $N/f$ can be interpreted in terms of the waves and vortices, and identify the main effects that can explain this transition based on both inviscid invariants arguments and viscous effects due to vertical shear.

Buoyancy effects in vertical shear dispersion

1992 ◽  
Vol 242 ◽  
pp. 371-386 ◽  
Author(s):  
Ronald Smith
Keyword(s):  
Vertical Plane ◽  
Solvable Model ◽  
Solution Procedure ◽  
Vertical Shear ◽  
Shear Dispersion ◽  
Exactly Solvable ◽  
Parallel Shear Flows ◽  
Miscible Fluid ◽  
Explicit Formulae ◽  
Nonlinear Shear

Density gradients modify the flow and hence the shear dispersion of one miscible fluid in another. A solution procedure is given for calculating the effects of weak buoyancy for vertical laminar parallel shear flows. A particular extrapolation to large buoyancy gives an exactly solvable nonlinear diffusion equation. For the particular case of vertical plane Poiseuille flow explicit formulae are derived for the flow, for the nonlinear shear dispersion coefficient and for the onset of instability. The exactly solvable model gives reasonably accurate results for the buoyancy-modified shear dispersion over a range from half to one-and-a-half times the non-buoyant value.

Frontogenesis in a fluid with horizontal density gradients

1989 ◽  
Vol 202 ◽  
pp. 1-16 ◽  
Author(s):  
J. E. Simpson ◽  
P. F. Linden
Keyword(s):  
Density Distribution ◽  
Density Gradient ◽  
Initial Density ◽  
Vertical Shear ◽  
Horizontal Gradient ◽  
Constant Density ◽  
Piecewise Constant ◽  
Vertical Density ◽  
Step Density ◽  
Horizontal Density Gradient

The adjustment under gravity of a fluid containing a horizontal density gradient is described.’ The fluid is initially at rest and the resulting motion is calculated as the flow accelerates, driven by the baroclinic density field. Two forms of the initial density distribution are considered. In the first the initial horizontal gradient is constant. A purely horizontal motion develops as the isopycnals rotate towards the horizontal. The vertical density gradient increases continually with time but the horizontal density gradient remains unchanged. The horizontal velocity has a uniform vertical shear, and the gradient Richardson number is constant in space and decreases monotonically with time to ½. The second density distribution consists of a piecewise constant gradient with a jump in the gradient along a vertical isopycnal. The density is continuous. In this case frontogenesis is predicted to occur on the isopycnal between the two constant-density-gradient regions, and the timescale for the formation of a front is determined. Laboratory experiments are reported which confirm the results of these calculations. In addition, lock exchange experiments have been carried out in which the horizontal mean gradient is represented by a series of step density differences separated by vertical gates.

Deformation Behavior of Cu-8wt%Ag Alloy during Equal Channel Angular Pressing

2015 ◽  
Vol 1101 ◽  
pp. 93-98
Author(s):  
Yue Shen ◽  
Chuan Ting Ren ◽  
Guo Quan Zhang ◽  
Ming Xie ◽  
Ming Wen ◽  
...  
Keyword(s):  
Shear Deformation ◽  
Equal Channel Angular Pressing ◽  
Deformation Behavior ◽  
Shear Bands ◽  
Vertical Plane ◽  
Vertical Shear ◽  
Ecap Processing ◽  
Angular Pressing ◽  
Micro Level ◽  
The One

The shear deformation behavior of the course-grained Cu-8wt%Ag alloy processed by one pass of equal channel angular pressing (ECAP) was revealed through the metallurgical microscope and the scanning electron microscope. Through the macro-level and micro-level synthesis analysis, it is confirmed that there are two shear deformation during the ECAP processing: the one along the intersection plane (IP) and the other along the vertical plane to the IP. And it is estimated that theoretical ranges of two shear angles are-32°<θ1<0° and 43°<θ2<58° respectively. Finally, it is also proved that the evolution of the shear bands is affected by the parallel and vertical shear to the IP of the ECAP die, and that, besides the shear along the IP, the shear along the vertical plane to the IP also plays an important role during the plastic deformation.

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

&lt;div&gt; &lt;div&gt; &lt;div&gt; &lt;p&gt;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.&lt;/p&gt; &lt;p&gt;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.&lt;/p&gt; &lt;/div&gt; &lt;/div&gt; &lt;/div&gt;

A rapidly convergent procedure for solving the equations of subsonic potential flow. I. Numerical solutions

1960 ◽  
Vol 255 (1280) ◽  
pp. 101-113 ◽  
Keyword(s):  
Potential Flow ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Local Density ◽  
Relaxation Method ◽  
Two Dimensional ◽  
Approximation Solution ◽  
Flow Equations ◽  
Bernoulli’S Equation ◽  
First Approximation

The subsonic potential flow equations for a perfect gas are transformed by means of dependent variables s = ( ρ / ρ 0 ) n q/ a 0 and σ = 1/2 In ( ρ 0 / ρ ), where q is the local velocity, ρ and a the local density and speed of sound, and the suffix 0 indicates stagnation conditions, n is a parameter which is to be chosen to optimize the approximations. Bernoulli’s equation then becomes a relation between s 2 and σ which is independent of initial conditions. A family of first-approximation solutions in terms of the incompressible solution is obtained on linearizing. It is shown that for two-dimensional flow, the choice n = 0∙5 gives results as accurate as those obtained with the Karman—Tsien solution. The exact equations are then transformed into the plane of the incompressible velocity potential and stream function and the first-approximation results substituted in the non ­linear terms. The resulting second-approximation equations can then be solved by a relaxation method and the error in this approximation estimated by carrying out the third-approximation solution. Results are given for a circular cylinder at a free-stream Mach number, M ∞ = 0∙4, and a sphere at M ∞ = 0∙5. The error in the velocity distribution is shown to be less than ±1 % in the two-dimensional case. A rough and ready compressibility rule is formulated for axisymmetric bodies, dependent on their thickness ratios.

scholarly journals A Potential Density Gradient Dependent Analysis Scheme for Ocean Multiscale Data Assimilation

2017 ◽  
Vol 2017 ◽  
pp. 1-13
Author(s):  
Hongli Fu ◽  
Jinkun Yang ◽  
Wei Li ◽  
Xinrong Wu ◽  
Guijun Han ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Density Gradient ◽  
Initial Conditions ◽  
Ocean Model ◽  
Potential Density ◽  
3 Dimensional ◽  
Ocean Data Assimilation ◽  
Variational Framework ◽  
Analysis Scheme ◽  
Density Surface

This study addresses how to maintain oceanic mixing along potential density surface in ocean data assimilation (ODA). It is well known that the oceanic mixing across the potential density surface is much weaker than that along the potential density surface. However, traditional ODA schemes allow the mixing across the potential density surface and thus may result in extra assimilation errors. Here, a new ODA scheme that uses potential density gradient information of the model background to rescale observational adjustment is designed to improve the quality of assimilation. The new scheme has been tested using a regional ocean model within a multiscale 3-dimensional variational framework. Results show that the new scheme effectively prevents the excessive unphysical projection of observational information in the direction across potential density surface and thus improves assimilation quality greatly. Forecast experiments also show that the new scheme significantly improves the model forecast skills through providing more dynamically consistent initial conditions

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