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热准地转模型的理论与计算分析

Theoretical and Computational Analysis of the Thermal Quasi-Geostrophic Model.

作者信息

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

机构信息

Department of Mathematics, Imperial College, London, SW7 2AZ UK.

Department of Mathematics, University of Twente, 7500 AE Enschede, The Netherlands.

出版信息

J Nonlinear Sci. 2023;33(5):96. doi: 10.1007/s00332-023-09943-9. Epub 2023 Aug 16.

DOI:10.1007/s00332-023-09943-9
PMID:37601550
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC10432375/
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 -TQG converge to solutions of TQG as its smoothing parameter and we obtain blow-up criteria for the -TQG model. The main contribution of the computational analysis is to verify the rate of convergence of -TQG solutions to TQG solutions as , for example, simulations in appropriate GFD regimes.

摘要

这项工作涉及亚中尺度地球物理流体动力学（GFD）的热准地转（TQG）模型的理论和数值分析。从物理角度来看，TQG模型涉及热地转平衡，其中罗斯比数、弗劳德数和分层参数都具有相同的渐近阶数。本文的主要分析贡献在于为TQG模型构造局部时间唯一强解。为此，我们证明了其正则化版本-TQG的解随着其平滑参数收敛到TQG的解，并且我们得到了-TQG模型的爆破准则。计算分析的主要贡献在于验证当 时，-TQG解到TQG解的收敛速率，例如在适当的GFD区域进行模拟。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9353/10432375/1284c528789f/332_2023_9943_Fig10_HTML.jpg
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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9353/10432375/2803d0951af4/332_2023_9943_Fig6_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9353/10432375/36dab6be071c/332_2023_9943_Fig7_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9353/10432375/1d426c8ef41e/332_2023_9943_Fig8_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9353/10432375/0e327424ed30/332_2023_9943_Fig9_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9353/10432375/1284c528789f/332_2023_9943_Fig10_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9353/10432375/5fc32c4f2efb/332_2023_9943_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9353/10432375/2ca14f6449bb/332_2023_9943_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9353/10432375/db90fbc47333/332_2023_9943_Fig3_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9353/10432375/242971b677e2/332_2023_9943_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9353/10432375/dee4c8be75e4/332_2023_9943_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9353/10432375/2803d0951af4/332_2023_9943_Fig6_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9353/10432375/36dab6be071c/332_2023_9943_Fig7_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9353/10432375/1d426c8ef41e/332_2023_9943_Fig8_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9353/10432375/0e327424ed30/332_2023_9943_Fig9_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9353/10432375/1284c528789f/332_2023_9943_Fig10_HTML.jpg

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本文引用的文献

1
Stochastic Variational Formulations of Fluid Wave-Current Interaction.流体波流相互作用的随机变分公式
J Nonlinear Sci. 2021;31(1):4. doi: 10.1007/s00332-020-09665-2. Epub 2020 Dec 18.
2
Variational principles for stochastic fluid dynamics.随机流体动力学的变分原理。
Proc Math Phys Eng Sci. 2015 Apr 8;471(2176):20140963. doi: 10.1098/rspa.2014.0963.