Balance in non-hydrostatic rotating shallow-water flows
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Unsteady nonlinear shallow-water flows typically emit inertia-gravity waves through a process called “spontaneous adjustment-emission.” This process has been studied extensively within the rotating shallow-water model, the simplest geophysical model having the required capability. Here, we consider what happens when the hydrostatic assumption underpinning the shallow-water model is dropped. This assumption is in fact not necessary for the derivation of a two-dimensional or single-layer flow model. All one needs is that the horizontal flow field be independent of height in the fluid layer. Then, vertical averaging yields a single-layer flow model with the full range of expected conservation laws, similar to the shallow-water model yet allowing for non-hydrostatic effects. These effects become important for horizontal scales comparable to or less than the depth of the fluid layer. In a rotating flow, such scales may be activated if the Rossby deformation length (the ratio of the characteristic gravity-wave speed to the Coriolis frequency) is comparable to the depth of the fluid layer. Then, the range of frequencies supporting inertia-gravity waves is compressed, and the group velocity of these waves is reduced. We find that this change in wave properties has the effect of strongly suppressing spontaneous adjustment-emission and trapping inertia-gravity waves near regions of relatively strong circulation.
Jalali , M R & Dritschel , D G 2021 , ' Balance in non-hydrostatic rotating shallow-water flows ' , Physics of Fluids , vol. 33 , no. 8 , 086601 . https://doi.org/10.1063/5.0057707
Physics of Fluids
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DescriptionFunding: The Leverhulme Trust (Grant Number(s) RF-2020-190).
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