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Abstract
Unsteady nonlinear shallowwater flows typically emit inertiagravity waves through a process called “spontaneous adjustmentemission.” This process has been studied extensively within the rotating shallowwater model, the simplest geophysical model having the required capability. Here, we consider what happens when the hydrostatic assumption underpinning the shallowwater model is dropped. This assumption is in fact not necessary for the derivation of a twodimensional or singlelayer flow model. All one needs is that the horizontal flow field be independent of height in the fluid layer. Then, vertical averaging yields a singlelayer flow model with the full range of expected conservation laws, similar to the shallowwater model yet allowing for nonhydrostatic 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 gravitywave speed to the Coriolis frequency) is comparable to the depth of the fluid layer. Then, the range of frequencies supporting inertiagravity 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 adjustmentemission and trapping inertiagravity waves near regions of relatively strong circulation.
Original language  English 

Article number  086601 
Number of pages  12 
Journal  Physics of Fluids 
Volume  33 
Issue number  8 
Early online date  3 Aug 2021 
DOIs  
Publication status  Published  3 Aug 2021 
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Dive into the research topics of 'Balance in nonhydrostatic rotating shallowwater flows'. Together they form a unique fingerprint.Projects
 1 Finished

A Fudemental reassessment of shallow: A Fundamental reassessment of shallowwater fluid dynamics
Dritschel, D. G. (PI)
1/01/21 → 31/12/21
Project: Fellowship