Dynamic Phase Alignment in Navier-Stokes Turbulence

TL;DR

This paper reveals that in Navier-Stokes turbulence, a scale-dependent phase alignment between velocity and vorticity fluctuations enables simultaneous energy and helicity cascades with a shared spectral scaling.

Contribution

It introduces the concept of phase alignment as a mechanism for compatible cascades in turbulence, supported by direct numerical simulations.

Findings

Phase alignment angle scales as rac{1}{k}

Energy and helicity cascades share rac{5}{3} spectral scaling

Phase alignment facilitates joint cascade compatibility

Abstract

In Navier-Stokes turbulence, energy and helicity injected at large scales are subject to a joint direct cascade, with both quantities exhibiting a spectral scaling $\propto k^{-5/3}$. We demonstrate via direct numerical simulations that the two cascades are compatible due to the existence of a strong scale-dependent phase alignment between velocity and vorticity fluctuations, with the phase alignment angle scaling as $\cos\alpha_k\propto k^{-1}$.