scholarly journals Single-particle Lagrangian statistics from direct numerical simulations of rotating-stratified turbulence

2020 ◽  
Vol 5 (6) ◽  
Author(s):  
D. Buaria ◽  
A. Pumir ◽  
F. Feraco ◽  
R. Marino ◽  
A. Pouquet ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Single Particle ◽  
Direct Numerical Simulations ◽  
Stratified Turbulence ◽  
Lagrangian Statistics

Potential enstrophy in stratified turbulence

2013 ◽  
Vol 722 ◽  
Author(s):  
Michael L. Waite
Keyword(s):  
Fluid Dynamics ◽  
Numerical Simulations ◽  
Reynolds Numbers ◽  
Direct Numerical Simulations ◽  
Quadratic Approximation ◽  
Stratified Turbulence ◽  
Geophysical Fluid Dynamics ◽  
Quadratic Part ◽  
Flow Variables ◽  
Potential Enstrophy

AbstractDirect numerical simulations are used to investigate potential enstrophy in stratified turbulence with small Froude numbers, large Reynolds numbers, and buoyancy Reynolds numbers ($R{e}_{b} $) both smaller and larger than unity. We investigate the conditions under which the potential enstrophy, which is a quartic quantity in the flow variables, can be approximated by its quadratic terms, as is often done in geophysical fluid dynamics. We show that at large scales, the quadratic fraction of the potential enstrophy is determined by $R{e}_{b} $. The quadratic part dominates for small $R{e}_{b} $, i.e. in the viscously coupled regime of stratified turbulence, but not when $R{e}_{b} \gtrsim 1$. The breakdown of the quadratic approximation is consistent with the development of Kelvin–Helmholtz instabilities, which are frequently observed to grow on the layerwise structure of stratified turbulence when $R{e}_{b} $ is not too small.

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.

scholarly journals Partitioning Waves and Eddies in Stably Stratified Turbulence

Atmosphere ◽  
2020 ◽  
Vol 11 (4) ◽  
pp. 420 ◽  
Author(s):  
Henri Lam ◽  
Alexandre Delache ◽  
Fabien S Godeferd
Keyword(s):  
Dispersion Relation ◽  
Kinetic Energy ◽  
Laminar Flow ◽  
Turbulent Flow ◽  
Numerical Simulations ◽  
Direct Numerical Simulations ◽  
Energy Concentration ◽  
Kinetic Energy Density ◽  
Stratified Turbulence ◽  
The Waves

We consider the separation of motion related to internal gravity waves and eddy dynamics in stably stratified flows obtained by direct numerical simulations. The waves’ dispersion relation links their angle of propagation to the vertical θ , to their frequency ω , so that two methods are used for characterizing wave-related motion: (a) the concentration of kinetic energy density in the ( θ , ω ) map along the dispersion relation curve; and (b) a direct computation of two-point two-time velocity correlations via a four-dimensional Fourier transform, permitting to extract wave-related space-time coherence. The second method is more computationally demanding than the first. In canonical flows with linear kinematics produced by space-localized harmonic forcing, we observe the pattern of the waves in physical space and the corresponding concentration curve of energy in the ( θ , ω ) plane. We show from a simple laminar flow that the curve characterizing the presence of waves is distorted differently in the presence of a background convective mean velocity, either uniform or varying in space, and also when the forcing source is moving. By generalizing the observation from laminar flow to turbulent flow, this permits categorizing the energy concentration pattern of the waves in complex flows, thus enabling the identification of wave-related motion in a general turbulent flow with stable stratification. The advanced method (b) is finally used to compute the wave-eddy partition in the velocity–buoyancy fields of direct numerical simulations of stably stratified turbulence. In particular, we use this splitting in statistics as varied as horizontal and vertical kinetic energy, as well as two-point velocity and buoyancy spectra.

scholarly journals Testing the Assumptions Underlying Ocean Mixing Methodologies Using Direct Numerical Simulations

2019 ◽  
Vol 49 (11) ◽  
pp. 2761-2779 ◽  
Author(s):  
J. R. Taylor ◽  
S. M. de Bruyn Kops ◽  
C. P. Caulfield ◽  
P. F. Linden
Keyword(s):  
Numerical Simulations ◽  
Field Measurements ◽  
Direct Numerical Simulations ◽  
Buoyancy Flux ◽  
Theoretical Development ◽  
Computational Domain ◽  
Vertical Profiles ◽  
Stratified Turbulence ◽  
Vertical Diffusivity ◽  
Thorpe Scale

AbstractDirect numerical simulations of stratified turbulence are used to test several fundamental assumptions involved in the Osborn, Osborn–Cox, and Thorpe methods commonly used to estimate the turbulent diffusivity from field measurements. The forced simulations in an idealized triply periodic computational domain exhibit characteristic features of stratified turbulence including intermittency and layer formation. When calculated using the volume-averaged dissipation rates from the simulations, the vertical diffusivities inferred from the Osborn and Osborn–Cox methods are within 40% of the value diagnosed using the volume-averaged buoyancy flux for all cases, while the Thorpe-scale method performs similarly well in the simulation with a relatively large buoyancy Reynolds number (Reb ≃ 240) but significantly overestimates the vertical diffusivity in simulations with Reb < 60. The methods are also tested using a limited number of vertical profiles randomly selected from the computational volume. The Osborn, Osborn–Cox, and Thorpe-scale methods converge to their respective estimates based on volume-averaged statistics faster than the vertical diffusivity calculated directly from the buoyancy flux, which is contaminated with reversible contributions from internal waves. When applied to a small number of vertical profiles, several assumptions underlying the Osborn and Osborn–Cox methods are not well supported by the simulation data. However, the vertical diffusivity inferred from these methods compares reasonably well to the exact value from the simulations and outperforms the assumptions underlying these methods in terms of the relative error. Motivated by a recent theoretical development, it is speculated that the Osborn method might provide a reasonable approximation to the diffusivity associated with the irreversible buoyancy flux.

scholarly journals Asymmetry of vertical buoyancy gradient in stratified turbulence

2019 ◽  
Vol 870 ◽  
pp. 266-289
Author(s):  
Andrea Maffioli
Keyword(s):  
Numerical Simulations ◽  
Isotropic Turbulence ◽  
Vertical Direction ◽  
Direct Consequence ◽  
Stable Stratification ◽  
Direct Numerical Simulations ◽  
Stratified Turbulence ◽  
Theoretical Predictions ◽  
Rapid Adjustment ◽  
Good Agreement

We consider the asymmetry of the buoyancy field in the vertical direction in stratified turbulence. While this asymmetry is known, its causes are not well understood, and it has not been systematically quantified previously. Using theoretical arguments, it is shown that both stratified turbulence and isotropic turbulence in the presence of a mean scalar gradient will become positively skewed, as a direct consequence of the presence of stratification and mean scalar gradient, respectively. Assuming a rapid adjustment of isotropic turbulence to a stable stratification on a time scale $\unicode[STIX]{x1D70F}\sim N^{-1}$, where $N$ is the Brunt–Väisälä frequency, a scaling for the skewness of the vertical buoyancy gradient is obtained. Direct numerical simulations of stratified turbulence with forcing are performed and the positive skewness of $\unicode[STIX]{x2202}b/\unicode[STIX]{x2202}z$ is confirmed ($b$ is the buoyancy). Both the volume-averaged dimensional skewness, $\langle (\unicode[STIX]{x2202}b/\unicode[STIX]{x2202}z)^{3}\rangle$, and the non-dimensional skewness, $S$, are computed and compared against the theoretical predictions. There is a good agreement for $\langle (\unicode[STIX]{x2202}b/\unicode[STIX]{x2202}z)^{3}\rangle$, while there is a discrepancy in the behaviour of $S$. The theory predicts $S\sim 1$ and a constant skewness, while the direct numerical simulations confirm that the skewness is $O(1)$ but with a remaining dependence on the Froude number. The results are interpreted as being due to the concurrent action of linear and nonlinear processes in stratified turbulence leading to $S>0$ and to the formation of layers and interfaces in vertical profiles of buoyancy.

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