Dynamic Scaling in Rotating Turbulence: A Shell Model Study

TL;DR

This paper studies the dynamic scaling behavior of rotating turbulence using a shell model, deriving and validating relations between dynamic and equal-time exponents through multifractal formalism and numerical simulations.

Contribution

It provides the first detailed theoretical and numerical analysis of dynamic exponents in rotating turbulence, linking them to equal-time exponents via multifractal formalism.

Findings

Derived relations between dynamic and equal-time exponents.

Validated theoretical predictions with extensive numerical simulations.

Enhanced understanding of time-scale behavior in rotating turbulent flows.

Abstract

We investigate the scaling form of appropriate time-scales extracted from time-dependent correlation functions in rotating, turbulent flows. In particular, we obtain precise estimates of the dynamic exponents $z_p$, associated with the time-scales, and their relation with the more commonly measured equal-time exponents $\zeta_p$. These theoretical predictions, obtained by using the multifractal formalism, are validated through extensive numerical simulations of a shell model for such rotating flows.