Spontaneous Gravity Wave Emission in the Differentially Heated Rotating Annulus

The source mechanism of inertia-gravity waves (IGWs) observed in numerical simulations of the differentially heated rotating annulus experiment is investigated. The focus is on the wave generation from the balanced part of the flow, a process presumably contributing significantly to the atmospheric IGW field. Direct numerical simulations are performed for an atmosphere-like configuration of the annulus and possible regions of IGW activity are characterised by a Hilbert-transform algorithm. In addition, the flow is separated into a balanced and unbalanced part, assuming the limit of a small Rossby number, and the forcing of IGWs by the balanced part of the flow is derived rigorously. Tangent-linear simulations are then used to identify the part of the IGW signal that is rather due to radiation by the internal balanced flow than to boundary-layer instabilities at the side walls. An idealised fluid setup without rigid horizontal boundaries is considered as well, to see the effect of the identified balanced forcing unmasked by boundary-layer effects. The direct simulations of the realistic and idealised fluid setups show a clear baroclinic wave structure exhibiting a jet-front system similar to its atmospheric counterparts, superimposed by four distinct IGW packets. The subsequent tangent-linear analysis indicates that two wave packets are radiated from the internal flow, one is affected both by the internal flow and by the boundary layer and a fourth one is probably caused by boundary layer instabilities. The forcing by the balanced part of the flow is found to play a significant role in the generation of IGWs so that it supplements boundary-layer instabilities as key factor in the IGW emission in the differentially heated rotating annulus.