Direct numerical simulation of transitions towards structural vacillation in an air-filled, rotating, baroclinic annulus

Abstract

The route to chaos of baroclinic waves in a rotating, stratified fluid subjected to lateral heating can occur via several possible routes, involving either low-dimensional, quasiperiodic states or via a series of secondary small-scale instabilities. In a recent paper, we have discussed direct numerical simulations (DNS) of the low-dimensional route to chaos in a baroclinic annulus filled with air as the working fluid and compared results to those obtained in the laboratory for high Prandtl number liquids. In the present paper, we consider further DNS in the air-filled annulus at higher rotation rates. A transition in the flow structure is observed, where the centrifugal acceleration exceeds gravity and the dominant physical process changes from baroclinic instability to convection due to radial buoyancy. The transition of this convection to chaotic behavior is fundamentally different from that observed in the transition to the chaotic flow observed at lower rotation rates. Rather than via a sequence of low-dimensional, quasiperiodic states, the large-scale convection developed small-scale instabilities, which has been previously suggested as the origin of structural vacillation on the transition to geostrophic turbulence.