Theoretical and Computational Analysis of the Thermal Quasi-Geostrophic Model

• Published in: Journal of nonlinear science Vol. 33; no. 5; p. 96
• Main Authors: Crisan, D., Holm, D. D., Luesink, E., Mensah, P. R., Pan, W.
• Format: Journal Article
• Language: English
• Published: New York Springer US 2023; Springer Nature B.V
• Subjects: Analysis; Classical Mechanics; Convergence; Economic Theory/Quantitative Economics/Mathematical Methods; Fluid dynamics; Froude number; Geophysical fluids; Mathematical and Computational Engineering; Mathematical and Computational Physics; Mathematical models; Mathematics; Mathematics and Statistics; Numerical analysis; Parameters; Theoretical; 65D30; 76U50; 76U65; 86A05; Analysis of partial differential equations; Potential vorticity; 35R99; Rossby waves; Bathymetry; 65M60; Oceanography; Finite element methods
• ISSN: 0938-8974; 1432-1467
• DOI: 10.1007/s00332-023-09943-9

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.