Direct Statistical Simulation of the Busse Annulus

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.

arXiv comment11 pages, 6 figures

References in corpus (10)

• Dedalus: A Flexible Framework for Numerical Simulations with Spectral Methods
• Color of turbulence
• Direct Statistical Simulation of Out-of-Equilibrium Jets
• Statistics of an Unstable Barotropic Jet from a Cumulant Expansion
• Convectively driven shear and decreased heat flux
• Emergence and equilibration of jets in beta-plane turbulence: applications of Stochastic Structural Stability Theory
• Recent Developments in Theories of Inhomogeneous and Anisotropic Turbulence
• Statistical State Dynamics: a new perspective on turbulence in shear flow
• Vertically Sheared Horizontal Flow-Forming Instability in Stratified Turbulence: Analytical Linear Stability Analysis of Statistical State Dynamics Equilibria
• Direct statistical simulation of the Lorenz63 system

Cited by in corpus (2)

• Seven decades of exploring planetary interiors with rotating convection experiments
• Direct Statistical Simulation Using Generalised Cumulant Expansions