Coherent vortex extraction and simulation of 2D isotropic turbulence

Abstract

We present a method to extract coherent vortices out of turbulent flows, based on thresholding the wavelet coefficients of vorticity. We compare two ways of choosing the threshold and show how one can thus split each flow realization into coherent vortices and quasi-Gaussian white noise. We then describe a new method, called CVS (coherent vortex simulation), for computing deterministically the time evolution of the coherent vortices while neglecting or modelling the incoherent background noise. We develop a hierarchy of model equations based on the nonlinear Galerkin approach. In the first CVS method there is no modelling of the effect of the discarded coefficients and filtering out the incoherent background at each time step plays the role of turbulent dissipation. For the second approach we derive an additional linear equation to compute the effect of the incoherent background flow whose coefficients have been discarded. Finally, to validate both CVS approaches, we analyse the different terms of the filtered equations and present different simulations of homogeneous isotropic turbulence.

Keywords:

• computational fluid dynamics
• turbulence modelling
• coherent vortices
• coherent vortex simulation
• wavelets
• turbulence

Acknowledgements

K.S. thankfully acknowledges fruitful discussion with E. Titi and financial support from the Center for Nonlinear Studies, Los Alamos.