# Consistent shallow-water equations on the rotating sphere with complete Coriolis force and topography

@article{Tort2014ConsistentSE, title={Consistent shallow-water equations on the rotating sphere with complete Coriolis force and topography}, author={Marine Tort and Thomas Dubos and François Bouchut and Vladimir Zeitlin}, journal={Journal of Fluid Mechanics}, year={2014}, volume={748}, pages={789 - 821} }

Abstract Consistent shallow-water equations are derived on the rotating sphere with topography retaining the Coriolis force due to the horizontal component of the planetary angular velocity. Unlike the traditional approximation, this ‘non-traditional’ approximation captures the increase with height of the solid-body velocity due to planetary rotation. The conservation of energy, angular momentum and potential vorticity are ensured in the system. The caveats in extending the standard shallow…

## 16 Citations

Dynamically consistent shallow‐atmosphere equations with a complete Coriolis force

- Physics, Environmental Science
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Shallow‐atmosphere equations retaining both the vertical and horizontal components of the Coriolis force (the latter being neglected in the traditional approximation) are obtained. The derivation…

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- Geology
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The shallow‐water equations in spherical geometry have proven to be an invaluable prototypical tool to advance geophysical fluid dynamics. Many of the fundamental terms and properties, including…

Variational Principles in Geophysical Fluid Dynamics and Approximated Equations

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In this chapter, the variational principle of Hamilton is applied to different examples from Geophysical Fluid Dynamics. Hamilton’s principle is extended to uniformly rotating flows and to…

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Using the salient properties of the flow observed in the equatorial Pacific as a guide, an asymptotic procedure is applied to the Euler equation written in a suitable rotating frame. Starting from…

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- 2016

Symmetric and asymmetric inertial instability of the westerly mid-latitude barotropic Bickley jet is analysed without the traditional approximation which neglects the vertical component of the…

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The zonally symmetric inertial instability of oceanic near-equatorial flows is studied through high-resolution numerical simulations. In homogeneous upper layers, the instability of surface-confined…

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- Physics
- 2015

Abstract. The design of the icosahedral dynamical core DYNAMICO is presented. DYNAMICO solves the multi-layer rotating shallow-water equations, a compressible variant of the same equivalent to a…

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- Environmental Science, PhysicsGeophysical & Astrophysical Fluid Dynamics
- 2020

Two common approximations to the full Shallow Water Equations (SWEs) are non-divergence and quasi-geostrophy, and the degree to which these approximations lead to biases in numerical solutions are…

A variational formulation of geophysical fluid motion in non‐Eulerian coordinates

- Geology
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Systematic methods to derive geophysical equations of motion possessing conservation laws for energy, momentum and potential vorticity have recently been developed. One approach is based on…

Unidirectional Modes Induced by Nontraditional Coriolis Force in Stratified Fluids.

- Physics, Environmental SciencePhysical review letters
- 2022

Using topology, we unveil the existence of new unidirectional modes in compressible rotating stratified fluids. We relate their emergence to the breaking of time-reversal symmetry by rotation and…

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