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Balance in non-hydrostatic rotating shallow-water flows

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Jalali_2021_VA_Balance_Imbalance_PhysFluid_AAM.pdf (9.081Mb)
Date
03/08/2021
Author
Jalali, M.R.
Dritschel, David Gerard
Funder
The Leverhulme Trust
Grant ID
RF-2020-190
Keywords
QC Physics
T-NDAS
MCC
Metadata
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Abstract
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.
Citation
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
Publication
Physics of Fluids
Status
Peer reviewed
DOI
https://doi.org/10.1063/5.0057707
ISSN
1070-6631
Type
Journal article
Rights
Copyright © 2021 the Author(s). Published under exclusive licence by AIP Publishing. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1063/5.0057707.
Description
Funding: The Leverhulme Trust (Grant Number(s) RF-2020-190).
Collections
  • University of St Andrews Research
URI
http://hdl.handle.net/10023/23540

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