Sign cancellation and scaling in the vertical component of velocity and vorticity in rotating turbulence

TL;DR

This study investigates how rotation influences sign changes and scaling laws in the velocity and vorticity components of turbulence, revealing that vertical components exhibit distinct scaling behaviors under rotation.

Contribution

It provides high-resolution numerical evidence that vertical velocity and vorticity components follow specific scaling laws in rotating turbulence, supporting theories of their shared dynamics under strong rotation.

Findings

Vertical components show clear scaling laws under rotation.

Horizontal components remain smooth and do not fluctuate rapidly.

Vertical velocity and vorticity share the same scaling within error bars.

Abstract

We study sign changes and scaling laws in the Cartesian components of the velocity and vorticity of rotating turbulence, in the helicity, and in the components of vertically-averaged fields. Data for the analysis is provided by high-resolution direct numerical simulations of rotating turbulence with different forcing functions, with up to 1536^3 grid points, with Reynolds numbers between ~1100 and ~5100, and with moderate Rossby numbers between ~0.06 and ~8. When rotation is negligible, all Cartesian components of the velocity show similar scaling, in agreement with the expected isotropy of the flow. However, in the presence of rotation only the vertical components of the fields show clear scaling laws, with evidence of possible sign singularity in the limit of infinite Reynolds number. Horizontal components of the velocity are smooth and do not display rapid fluctuations for arbitrarily small scales. The vertical velocity and vorticity, as well as the vertically-averaged vertical velocity and vorticity, show the same scaling within error bars, in agreement with theories that predict that these quantities have the same dynamical equation for very strong rotation.