Direct Statistical Simulation of the Busse Annulus

TL;DR

This paper develops a direct statistical simulation approach for the Busse Annulus convection model, capturing complex jet dynamics and bursting behavior by expanding around the mean flow using cumulants, specifically CE2.

Contribution

It introduces a cumulant expansion-based DSS method for the Busse Annulus, demonstrating its ability to reproduce complex flow phenomena with a quasi-linear CE2 approach.

Findings

CE2 reproduces direct numerical simulation results for jet dynamics.

Symmetry considerations are crucial for accurate CE2 modeling.

CE2 captures bursting and bistable jet behaviors.

Abstract

We consider direct statistical simulation (DSS) of a paradigm system of convection interacting with mean flows. In the Busse Annulus model zonal jets are generated through the interaction of convectively driven turbulence and rotation; non-trivial dynamics including the emergence of multiple jets and bursting `predator-prey' type dynamics can be found. We formulate the DSS by expanding around the mean flow in terms of equal-time cumulants and arrive at a closed set of equations of motion for the cumulants. Here, we present results using an expansion terminated at the second cumulant (CE2); it is fundamentally a quasi-linear theory. We focus on particular cases including bursting and bistable multiple jets and demonstrate that CE2 can reproduce the results of direct numerical simulation if particular attention is given to symmetry considerations.