Stochastic mesoscale circulation dynamics in the thermal ocean
File(s)
Accepted version
Author(s)
Holm, Darryl
Luesink, Erwin
Pan, Wei
Type
Journal Article
Abstract
In analogy with similar effects in adiabatic compressible fluid dynamics, the effects of buoyancy gradients on incompressible stratified flows are said to be “thermal.” The thermal rotating shallow water (TRSW) model equations contain three small nondimensional parameters. These are the Rossby number, the Froude number, and the buoyancy parameter. Asymptotic expansion of the TRSW model equations in these three small parameters leads to the deterministic thermal versions of the Salmon’s L1 (TL1) model and the thermal quasi-geostrophic (TQG) model, upon expanding in the neighborhood of thermal quasi-geostrophic balance among the flow velocity and the gradients of free surface elevation and buoyancy. The linear instability of TQG at high wavenumber tends to create circulation at small scales. Such a high- wavenumber instability could be unresolvable in many computational simulations, but its presence at small scales may contribute signifi- cantly to fluid transport at resolvable scales. Sometimes, such effects are modeled via “stochastic backscatter of kinetic energy.” Here, we try another approach. Namely, we model “stochastic transport” in the hierarchy of models TRSW/TL1/TQG. The models are derived via the approach of stochastic advection by Lie transport (SALT) as obtained from a recently introduced stochastic version of the Euler–Poincare var- iational principle. We also indicate the potential next steps for applying these models in uncertainty quantification and data assimilation of the rapid, high-wavenumber effects of buoyancy fronts at these three levels of description by using the data-driven stochastic parametrization algorithms derived previously using the SALT approach.
Editor(s)
Giacomin, Alan Jeffrey
Date Issued
2021-04-07
Date Acceptance
2021-02-12
Citation
Physics of Fluids, 2021, 33 (4), pp.1-22
ISSN
1070-6631
Publisher
American Institute of Physics
Start Page
1
End Page
22
Journal / Book Title
Physics of Fluids
Volume
33
Issue
4
Copyright Statement
© 2021 Author(s). Published under license by AIP Publishing. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Physics of Fluids 33, 046603 (2021) and may be found at https://doi.org/10.1063/5.0040026
Sponsor
Commission of the European Communities
Identifier
https://aip.scitation.org/doi/10.1063/5.0040026
Grant Number
856408
Subjects
physics.flu-dyn
physics.flu-dyn
physics.geo-ph
Fluids & Plasmas
01 Mathematical Sciences
02 Physical Sciences
09 Engineering
Publication Status
Published
Article Number
046603
Date Publish Online
2021-04-07