The TRR 181 seminar is held by Dr. Manita Chouksey on January 20, 11am.

Does an interface exist, and what is it's role, between the slow and fast manifolds?

Abstract

The balanced state in geophysical flows, such as the atmosphere and ocean, largely describes the dynamics and energetics of the low frequency flow. The unique depiction and diagnosis of this balanced state, or the so-called 'slow manifold', however remains conflicted. At the same time, the co-existing unbalanced high-frequency motions, or the 'fast manifold', also significantly influence the energetics of the flow. This co-existence of the balanced and unbalanced modes suggests the likelihood of the existence of an interface between the slow and fast manifolds, with a crucial role in energy transfers and exchanges that dictate the flow dynamics. However the identification, interpretation, and the interaction between these modes rely on the precise separation of the balanced and unbalanced modes, that remains complex and challenging. 
 
Different flow decomposition methods are implemented in a numerical model of baroclinic instability, for a range of flow regimes characterized by the Rossby number, for the classical case of spontaneous emission. The first method uses the non-linear modal decomposition of Machenhauer (1977), further extended to higher orders in Ro. In the former case the unbalanced state still comprises of slaved modes, which could be associated with the interface between the two manifolds. At higher orders in Ro , however, and a more precise balanced state is achieved (Eden et al. 2019). Further, the balanced state obtained from this procedure is compared to the one obtained from the optimal balance procedure. Both the methods produce a precise balanced state but the comparison reveals the dependence of the balanced state on the numerics. The results also suggest a weak importance of spontaneous loss of balance in comparison to convective or symmetric instabilities for internal wave generation. Wave generation in the case of stimulated emission is also explored. Overall, the results have implications for the generation and dissipation of the balanced and unbalanced modes, as well as for the interactions and energy transfers between them that form a key constituent of the flow's energy cycle. The question of the existence of an interface between the two manifolds continues to be intriguing and remains open for further  exploration.