Theoretical and computational analysis of the thermal quasi-geostrophic model
File(s)
Author(s)
Crisan, D
Holm, DD
Luesink, E
Mensah, PR
Pan, W
Type
Journal Article
Abstract
This work involves theoretical and numerical analysis of the thermal quasi-geostrophic
(TQG) model of submesoscale geophysical fluid dynamics (GFD). Physically, the
TQG model involves thermal geostrophic balance, in which the Rossby number, the
Froude number and the stratification parameter are all of the same asymptotic order.
The main analytical contribution of this paper is to construct local-in-time unique
strong solutions for the TQG model. For this, we show that solutions of its regularised
version α-TQG converge to solutions of TQG as its smoothing parameter α → 0
and we obtain blow-up criteria for the α-TQG model. The main contribution of the
computational analysis is to verify the rate of convergence of α-TQG solutions to TQG
solutions as α → 0, for example, simulations in appropriate GFD regimes.
(TQG) model of submesoscale geophysical fluid dynamics (GFD). Physically, the
TQG model involves thermal geostrophic balance, in which the Rossby number, the
Froude number and the stratification parameter are all of the same asymptotic order.
The main analytical contribution of this paper is to construct local-in-time unique
strong solutions for the TQG model. For this, we show that solutions of its regularised
version α-TQG converge to solutions of TQG as its smoothing parameter α → 0
and we obtain blow-up criteria for the α-TQG model. The main contribution of the
computational analysis is to verify the rate of convergence of α-TQG solutions to TQG
solutions as α → 0, for example, simulations in appropriate GFD regimes.
Date Issued
2023-10
Date Acceptance
2023-07-07
Citation
Journal of Nonlinear Science, 2023, 33 (5)
ISSN
0938-8974
Publisher
Springer
Journal / Book Title
Journal of Nonlinear Science
Volume
33
Issue
5
Copyright Statement
© The Author(s) 2023
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
License URL
Identifier
https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:001049805900001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=a2bf6146997ec60c407a63945d4e92bb
Subjects
Analysis of partial differential equations
Bathymetry
DYNAMICS
EQUATIONS
EULER
Finite element methods
Mathematics
Mathematics, Applied
Mechanics
OCEAN MODEL
Oceanography
Physical Sciences
Physics
Physics, Mathematical
Potential vorticity
Rossby waves
Science & Technology
Technology
VARIABILITY
Publication Status
Published
Article Number
96
Date Publish Online
2023-08-16