Theoretical and Computational Analysis of the Thermal Quasi-Geostrophic Model

D. Crisan, D.D. Holm, E. Luesink*, P.R. Mensah, W. Pan

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)
4 Downloads (Pure)

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.

Original languageEnglish
Article number96
JournalJournal of nonlinear science
Volume33
Issue number5
DOIs
Publication statusPublished - Oct 2023

Keywords

  • Analysis of partial differential equations
  • Bathymetry
  • Finite element methods
  • Oceanography
  • Potential vorticity
  • Rossby waves
  • UT-Hybrid-D

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