Vortex stretching and enstrophy production in high Reynolds number turbulence

Abstract

An essential ingredient of turbulent flows is the vortex stretching mechanism, which emanates from the non-linear interaction of vorticity and strain-rate tensor and leads to formation of extreme events. We analyze the statistical correlations between vorticity and strain rate by using a massive database generated from very well resolved direct numerical simulations of forced isotropic turbulence in periodic domains. The grid resolution is up to $12288^3$, and the Taylor-scale Reynolds number is in the range $140-1300$. In order to understand the formation and structure of extreme vorticity fluctuations, we obtain statistics conditioned on enstrophy (vorticity-squared). The magnitude of strain, as well as its eigenvalues, is approximately constant when conditioned on weak enstrophy; whereas they grow approximately as power laws for strong enstrophy, which become steeper with increasing $R_{\lambda }$. We find that the well-known preferential alignment between vorticity and the intermediate eigenvector of strain tensor is even stronger for large enstrophy, whereas vorticity shows a tendency to be weakly orthogonal to the most extensive eigenvector (for large enstrophy). Yet the dominant contribution to the production of large enstrophy events arises from the most extensive eigendirection, the more so as $R_{\lambda }$ increases. Nevertheless, the stretching in intense vorticity regions is significantly depleted, consistent with the kinematic properties of weakly-curved tubes in which they are organized. Further analysis reveals that intense enstrophy is primarily depleted via viscous diffusion, though viscous dissipation is also significant. Implications for modeling are nominally addressed as appropriate.

arXiv comment17 pages, 8 figures

References in corpus (7)

• The multifractal nature of turbulent energy dissipation
• Extreme velocity gradients in turbulent flows
• Is vortex stretching the main cause of the turbulent energy cascade?
• Direct Assessment of Vorticity Alignment with Local and Nonlocal Strain Rates in Turbulent Flows
• Dissipation range of the energy spectrum in high Reynolds number turbulence
• Dynamical Origins for Non-Gaussian Vorticity Distributions in Turbulent Flows
• Viscous tilting and production of vorticity in homogeneous turbulence

Cited by in corpus (25)

• Self-attenuation of extreme events in Navier-Stokes turbulence
• Forecasting small scale dynamics of fluid turbulence using deep neural networks
• An experimental study on the multiscale properties of turbulence in bubble-laden flows
• Turbulence is an ineffective mixer when Schmidt numbers are large
• Vorticity-strain rate dynamics and the smallest scales of turbulence
• Generation of intense dissipation in high Reynolds number turbulence
• Scaling of acceleration statistics in high Reynolds number turbulence
• Intermittency of turbulent velocity and scalar fields using 3D local averaging
• Non-local amplification of intense vorticity in turbulent flows
• Low-order moments of the velocity gradient in homogeneous compressible turbulence
• Saturation and multifractality of Lagrangian and Eulerian scaling exponents in 3D isotropic turbulence
• Dimension Reduced Turbulent Flow Data From Deep Vector Quantizers
• Lagrangian acceleration in fully developed turbulence and its Eulerian decompositions
• Analysis of pseudo-spectral methods used for numerical simulation of turbulence
• Role of pressure in generation of intense velocity gradients in turbulent flows
• Analysis of scale-dependent kinetic and potential energy in sheared, stably stratified turbulence
• Twisting vortex lines regularize Navier-Stokes turbulence
• Universality of extreme events in turbulent flows
• Cascades and Kolmogorov's lognormal scaling in two-dimensional bacterial turbulence
• Experimental measurement of the vorticity-strain alignment around extreme energy transfer events
• Demonstration of the rotational viscosity transfer across scales in Navier-Stokes turbulence
• Deformation of drops by outer eddies in turbulence
• Comparing velocity and passive scalar statistics in fluid turbulence at high Schmidt numbers and Reynolds numbers
• Band-Limited Equivalence of Convolution Operators and its Application to Filtered Vorticity Dynamics
• Critical transition to a non-chaotic regime in isotropic turbulence