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Thursday 24 Sep 2020Nonlinear resonance in the persistence of layers in stably-stratified fluids

Dr, Paul Burns - University of Exeter

Online 14:30-16:30

Stably-stratified flows allow the creation of mixed-layers separated by interfaces, called ‘staircases’, which have been observed to persist for long times in many fluid systems. To examine the role of oscillations in the persistence of these layers we derive an alternative form of the governing equations, without assuming weak nonlinearity, called the ‘modulation equations’, which reveals that the nonlinear frequency interactions act in perpetuity and create a low-frequency mean flow (LFMF). Combining these concepts with numerical simulations inspired by the laboratory experiments of Park et al, we demonstrate that ultimately it is internal gravity waves (IGWs) which cause the persistence of the layers (the LFMF). We find that the LFMF undergoes an internal vibration which also contributes to the layer persistence (a self-excitation effect). We find that as the background restoring force (proportional to the background stratification N and invariant in time) becomes larger than our initial impulse the contribution of this internal vibration becomes dominant and becomes increasingly so with increasing N. This increase in internal vibration corresponds with a sharp increase in the number of layers. We demonstrate the two-way coupling between the fast waves and LFMF. We also show that linear waves generated from near-resonant nonlinearity, are present in the higher time derivative of the modulation equation.

Zoom meeting details:

Meeting ID: 964 1453 1177

Password: 294800

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