Predictability in Rotating Turbulence: Insights from a Shell Model Study

TL;DR

This study uses a shell model to analyze how rotation affects the predictability of turbulent flows, revealing a power-law increase in predictability time with rotation rate and scale-dependent behaviors.

Contribution

It provides new insights into the predictability scaling laws in rotating turbulence, including the effects of Rossby number and scale dependence, validated through numerical simulations.

Findings

Predictability time scales with Rossby number as a power law with exponent -2/3.

Error dynamics exhibit a freezing period before algebraic growth.

Finite size Lyapunov exponent scales inversely with error size in the Zeman range.

Abstract

We investigate the predictability aspects of rotating turbulent flows through extensive numerical simulations of a shell model of rotating turbulence. In particular, we measure the large-scale predictability time and find that it increases with rotation rate to satisfy a power law in Rossby number with a scaling exponent of $-2/3$. Intriguingly, we find that before entering the algebraic growth stage, the error dynamics freezes for a time period determined by the finite Rossby number. We further analyse the scale dependence of the predictability time and observe that it tends to become scale independent in the Zeman range as the Rossby number decreases. Finally, we compute the finite size Lyapunov exponent and validate the dimensional prediction of its scaling $\sim\delta^{-1}$ for large $\delta$ of the order of velocities in the Zeman range for small Rossby numbers.