Nonlocal amplification of intense vorticity in turbulent flows

Abstract

The nonlinear and nonlocal coupling of vorticity and strain rate constitutes a major hindrance in understanding the self-amplification of velocity gradients in turbulent fluid flows. Utilizing highly resolved direct numerical simulations of isotropic turbulence in periodic domains of up to 12288^{3} grid points and Taylor-scale Reynolds number R_{λ} in the range 140–1300, we investigate this nonlocality by decomposing the strain-rate tensor into local and nonlocal contributions obtained through Biot-Savart integration of vorticity in a sphere of radius R. We find that vorticity is predominantly amplified by the nonlocal strain coming beyond a characteristic scale size, which varies as a simple power law of vorticity magnitude. The underlying dynamics preferentially align vorticity with the most extensive eigenvector of nonlocal strain. The remaining local strain aligns vorticity with the intermediate eigenvector and does not contribute significantly to amplification; instead it surprisingly attenuates intense vorticity, leading to breakdown of the observed power law and ultimately also the scale invariance of vorticity amplification, with important implications for prevailing intermittency theories.