Direct Statistical Simulation of Out-of-Equilibrium Jets

TL;DR

This paper compares a second-order cumulant expansion method to direct numerical simulations for modeling jet formation on a beta-plane, showing CE2's effectiveness near equilibrium and its limitations further from equilibrium.

Contribution

The study demonstrates the capabilities and limitations of CE2 in simulating jet dynamics and suggests including higher cumulants to improve accuracy.

Findings

CE2 reproduces jet structure near equilibrium.

CE2's accuracy decreases as jets deviate from equilibrium.

Higher cumulants may improve simulation accuracy.

Abstract

We present a Direct Statistical Simulation (DSS) of jet formation on a \beta-plane, solving for the statistics of a fluid flow via an expansion in cumulants. Here we compare an expansion truncated at second order (CE2) to statistics accumulated by direct numerical simulations (DNS). We show that, for jets near equilibrium, CE2 is capable of reproducing the jet structure (although some differences remain in the second cumulant). However as the degree of departure from equilibrium is increased (as measured by the zonostrophy parameter) the jets meander more and CE2 becomes less accurate. We discuss a possible remedy by inclusion of higher cumulants.