A Unified Formulation of Quasi-Geostrophic and Shallow Water Equations via Projection

IF 4.4 2区 地球科学 Q1 METEOROLOGY & ATMOSPHERIC SCIENCES
Louis Thiry, Long Li, Etienne Mémin, Guillaume Roullet
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Abstract

This paper introduces a unified model for layered rotating shallow-water (RSW) and quasi-geostrophic (QG) equations, based on the intrinsic relationship between these two sets of equations. We propose a novel formulation of the QG equations as a projection of the RSW equations. This formulation uses the same prognostic variables as RSW, namely velocity and layer thickness, thereby restoring the proximity of these two sets of equations. It provides direct access to the ageostrophic velocities embedded within the geostrophic velocities resolved by the QG equations. This approach facilitates the study of differences between QG and RSW using a consistent numerical discretization. We demonstrate the effectiveness of this formulation through examples including vortex shear instability, double-gyre circulation, and a simplified North Atlantic configuration.

Abstract Image

通过投影统一计算准地泳方程和浅水方程
本文基于分层旋转浅水(RSW)方程和准地转(QG)方程之间的内在联系,介绍了这两组方程的统一模型。我们提出了一种 QG 方程的新表述,作为 RSW 方程的投影。该公式使用了与 RSW 相同的预报变量,即速度和层厚度,从而恢复了这两套方程的接近性。它提供了直接获取 QG 方程所解析的地转速度中蕴含的老化速度的途径。这种方法便于使用一致的数值离散方法研究 QG 和 RSW 之间的差异。我们通过涡切不稳定性、双蕊环流和简化的北大西洋构型等示例证明了这种计算方法的有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Journal of Advances in Modeling Earth Systems
Journal of Advances in Modeling Earth Systems METEOROLOGY & ATMOSPHERIC SCIENCES-
CiteScore
11.40
自引率
11.80%
发文量
241
审稿时长
>12 weeks
期刊介绍: The Journal of Advances in Modeling Earth Systems (JAMES) is committed to advancing the science of Earth systems modeling by offering high-quality scientific research through online availability and open access licensing. JAMES invites authors and readers from the international Earth systems modeling community. Open access. Articles are available free of charge for everyone with Internet access to view and download. Formal peer review. Supplemental material, such as code samples, images, and visualizations, is published at no additional charge. No additional charge for color figures. Modest page charges to cover production costs. Articles published in high-quality full text PDF, HTML, and XML. Internal and external reference linking, DOI registration, and forward linking via CrossRef.
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