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.

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 Triadic resonances in precessing rapidly rotating cylinder flows

2015 ◽  
Vol 778 ◽  
Author(s):  
T. Albrecht ◽  
H. M. Blackburn ◽  
J. M. Lopez ◽  
R. Manasseh ◽  
P. Meunier
Keyword(s):  
Rotating Cylinder ◽  
Direct Numerical Simulations ◽  
Mode Shapes ◽  
Resonance Model ◽  
Rapid Rotation ◽  
Nutation Angle ◽  
Resonant Instability ◽  
Theoretical Predictions ◽  
Long Time ◽  
Good Agreement

Direct numerical simulations of flows in cylinders subjected to both rapid rotation and axial precession are presented and analysed in the context of a stability theory based on the triadic resonance of Kelvin modes. For a case that was chosen to provide a finely tuned resonant instability with a small nutation angle, the simulations are in good agreement with the theory and previous experiments in terms of mode shapes and dynamics, including long-time-scale regularization of the flow and recurrent collapses. Cases not tuned to the most unstable triad, but with the nutation angle still small, are also in quite good agreement with theoretical predictions, showing that the presence of viscosity makes the physics of the triadic-resonance model robust to detuning. Finally, for a case with $45^{\circ }$ nutation angle for which it has been suggested that resonance does not occur, the simulations show that a slowly growing triadic resonance predicted by theory is in fact observed if sufficient evolution time is allowed.

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.

Stochastic theory and direct numerical simulations of the relative motion of high-inertia particle pairs in isotropic turbulence

2017 ◽  
Vol 813 ◽  
pp. 205-249 ◽  
Author(s):  
Rohit Dhariwal ◽  
Sarma L. Rani ◽  
Donald L. Koch
Keyword(s):  
Numerical Simulations ◽  
Relative Motion ◽  
Relative Velocity ◽  
Isotropic Turbulence ◽  
Stochastic Theory ◽  
Stokes Number ◽  
Time Correlation ◽  
Direct Numerical Simulations ◽  
Time Integral ◽  
Particle Pairs

The relative velocities and positions of monodisperse high-inertia particle pairs in isotropic turbulence are studied using direct numerical simulations (DNS), as well as Langevin simulations (LS) based on a probability density function (PDF) kinetic model for pair relative motion. In a prior study (Rani et al., J. Fluid Mech., vol. 756, 2014, pp. 870–902), the authors developed a stochastic theory that involved deriving closures in the limit of high Stokes number for the diffusivity tensor in the PDF equation for monodisperse particle pairs. The diffusivity contained the time integral of the Eulerian two-time correlation of fluid relative velocities seen by pairs that are nearly stationary. The two-time correlation was analytically resolved through the approximation that the temporal change in the fluid relative velocities seen by a pair occurs principally due to the advection of smaller eddies past the pair by large-scale eddies. Accordingly, two diffusivity expressions were obtained based on whether the pair centre of mass remained fixed during flow time scales, or moved in response to integral-scale eddies. In the current study, a quantitative analysis of the (Rani et al. 2014) stochastic theory is performed through a comparison of the pair statistics obtained using LS with those from DNS. LS consist of evolving the Langevin equations for pair separation and relative velocity, which is statistically equivalent to solving the classical Fokker–Planck form of the pair PDF equation. Langevin simulations of particle-pair dispersion were performed using three closure forms of the diffusivity – i.e. the one containing the time integral of the Eulerian two-time correlation of the seen fluid relative velocities and the two analytical diffusivity expressions. In the first closure form, the two-time correlation was computed using DNS of forced isotropic turbulence laden with stationary particles. The two analytical closure forms have the advantage that they can be evaluated using a model for the turbulence energy spectrum that closely matched the DNS spectrum. The three diffusivities are analysed to quantify the effects of the approximations made in deriving them. Pair relative-motion statistics obtained from the three sets of Langevin simulations are compared with the results from the DNS of (moving) particle-laden forced isotropic turbulence for $St_{\unicode[STIX]{x1D702}}=10,20,40,80$ and $Re_{\unicode[STIX]{x1D706}}=76,131$. Here, $St_{\unicode[STIX]{x1D702}}$ is the particle Stokes number based on the Kolmogorov time scale and $Re_{\unicode[STIX]{x1D706}}$ is the Taylor micro-scale Reynolds number. Statistics such as the radial distribution function (RDF), the variance and kurtosis of particle-pair relative velocities and the particle collision kernel were computed using both Langevin and DNS runs, and compared. The RDFs from the stochastic runs were in good agreement with those from the DNS. Also computed were the PDFs $\unicode[STIX]{x1D6FA}(U|r)$ and $\unicode[STIX]{x1D6FA}(U_{r}|r)$ of relative velocity $U$ and of the radial component of relative velocity $U_{r}$ respectively, both PDFs conditioned on separation $r$. The first closure form, involving the Eulerian two-time correlation of fluid relative velocities, showed the best agreement with the DNS results for the PDFs.

The analysis and modelling of dilatational terms in compressible turbulence

1991 ◽  
Vol 227 ◽  
pp. 473-493 ◽  
Author(s):  
S. Sarkar ◽  
G. Erlebacher ◽  
M. Y. Hussaini ◽  
H. O. Kreiss
Keyword(s):  
Asymptotic Analysis ◽  
Numerical Simulations ◽  
Isotropic Turbulence ◽  
Stokes Equations ◽  
Mixing Layer ◽  
Direct Numerical Simulations ◽  
Homogeneous Turbulence ◽  
Compressible Turbulence ◽  
Quasi Equilibrium ◽  
Compressible Mixing Layer

It is shown that the dilatational terms that need to be modelled in compressible turbulence include not only the pressure-dilatation term but also another term - the compressible dissipation. The nature of the compressible velocity field, which generates these dilatational terms, is explored by asymptotic analysis of the compressible Navier-Stokes equations in the case of homogeneous turbulence. The lowest-order equations for the compressible field are solved and explicit expressions for some of the associated one-point moments are obtained. For low Mach numbers, the compressible mode has a fast timescale relative to the incompressible mode. Therefore, it is proposed that, in moderate Mach number homogeneous turbulence, the compressible component of the turbulence is in quasi-equilibrium with respect to the incompressible turbulence. A non-dimensional parameter which characterizes this equilibrium structure of the compressible mode is identified. Direct numerical simulations (DNS) of isotropic, compressible turbulence are performed, and their results are found to be in agreement with the theoretical analysis. A model for the compressible dissipation is proposed; the model is based on the asymptotic analysis and the direct numerical simulations. This model is calibrated with reference to the DNS results regarding the influence of compressibility on the decay rate of isotropic turbulence. An application of the proposed model to the compressible mixing layer has shown that the model is able to predict the dramatically reduced growth rate of the compressible mixing layer.

scholarly journals Virtual motion of real particles

2010 ◽  
Vol 650 ◽  
pp. 1-4 ◽  
Author(s):  
G. TRYGGVASON
Keyword(s):  
Kinetic Energy ◽  
Numerical Simulations ◽  
Turbulent Kinetic Energy ◽  
Multiphase Flows ◽  
Isotropic Turbulence ◽  
Finite Size ◽  
Direct Numerical Simulations ◽  
Spherical Particles ◽  
Length Scale ◽  
Turbulent Eddies

Direct numerical simulations are rapidly becoming one of the most important techniques to examine the dynamics of multiphase flows. Lucci, Ferrante & Elghobashi (J. Fluid Mech., 2010, this issue, vol. 650, pp. 5–55) address several fundamental issues for spherical particles in isotropic turbulence. They show the importance of including the finite size of the particles and discuss how particles of a size comparable to the largest length scale at which viscosity substantially affects the turbulent eddies (i.e. the Taylor microscale) always increase the dissipation of turbulent kinetic energy.

scholarly journals Turbulent drag reduction by anisotropic permeable substrates – analysis and direct numerical simulations

2019 ◽  
Vol 875 ◽  
pp. 124-172 ◽  
Author(s):  
G. Gómez-de-Segura ◽  
R. García-Mayoral
Keyword(s):  
Drag Reduction ◽  
Numerical Simulations ◽  
Critical Value ◽  
Direct Numerical Simulations ◽  
Mean Flow ◽  
Turbulent Drag Reduction ◽  
Turbulent Drag ◽  
Theoretical Predictions ◽  
The Mean ◽  
The Difference

We explore the ability of anisotropic permeable substrates to reduce turbulent skin friction, studying the influence that these substrates have on the overlying turbulence. For this, we perform direct numerical simulations of channel flows bounded by permeable substrates. The results confirm theoretical predictions, and the resulting drag curves are similar to those of riblets. For small permeabilities, the drag reduction is proportional to the difference between the streamwise and spanwise permeabilities. This linear regime breaks down for a critical value of the wall-normal permeability, beyond which the performance begins to degrade. We observe that the degradation is associated with the appearance of spanwise-coherent structures, attributed to a Kelvin–Helmholtz-like instability of the mean flow. This feature is common to a variety of obstructed flows, and linear stability analysis can be used to predict it. For large permeabilities, these structures become prevalent in the flow, outweighing the drag-reducing effect of slip and eventually leading to an increase of drag. For the substrate configurations considered, the largest drag reduction observed is ${\approx}$20–25 % at a friction Reynolds number $\unicode[STIX]{x1D6FF}^{+}=180$.

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