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… Expand
View on Cambridge Press
perso-math.univ-mlv.fr
15 Citations
Background Citations
6
Methods Citations
1

15 Citations

Citation Type

Citation Type

Dynamically consistent shallow‐atmosphere equations with a complete Coriolis force
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… Expand
Dynamically consistent shallow‐water equation sets in non‐spherical geometry with latitudinal variation of gravity
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… Expand
Variational Principles in Geophysical Fluid Dynamics and Approximated Equations
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… Expand
A variational formulation of geophysical fluid motion in non‐Eulerian coordinates
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… Expand
A nonlinear, three-dimensional model for ocean flows, motivated by some observations of the Pacific Equatorial Undercurrent and thermocline
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… Expand
Symmetric and asymmetric inertial instability of zonal jets on the $f$ -plane with complete Coriolis force
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… Expand
Equatorial inertial instability with full Coriolis force
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… Expand
DYNAMICO-1.0, an icosahedral hydrostatic dynamical core designed for consistency and versatility
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… Expand
Barotropic instability of a zonal jet on the sphere: from non-divergence through quasi-geostrophy to shallow water
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… Expand
Dispersive shallow water wave modelling. Part III: Model derivation on a globally spherical geometry
The present article is the third part of a series of papers devoted to the shallow water wave modelling. In this part, we investigate the derivation of some long wave models on a deformed sphere. We… Expand
...
1
2
...

References

SHOWING 1-10 OF 35 REFERENCES
Shallow water equations with a complete Coriolis force and topography
This paper derives a set of two-dimensional equations describing a thin inviscid fluid layer flowing over topography in a frame rotating about an arbitrary axis. These equations retain various terms… Expand
Dynamically consistent, quasi-hydrostatic equations for global models with a complete representation of the Coriolis force
The spherical polar components of the Coriolis force consist of terms in sin ϕ and terms in cos ϕ, where ϕ is latitude (referred to the frame-rotation vector as polar axis). The cos ϕ Coriolis terms… Expand
Derivation of the Equations of Atmospheric Motion in Oblate Spheroidal Coordinates
Since Earth is more nearly an oblate spheroid than a sphere, it is of at least theoretical interest to develop the atmospheric equations of motion in spheroidal coordinates. In this system the… Expand
Nonlinear theory of geostrophic adjustment. Part 1. Rotating shallow-water model
We develop a theory of nonlinear geostrophic adjustment of arbitrary localized (i.e. finite-energy) disturbances in the framework of the non-dissipative rotating shallow-water dynamics. The only… Expand
Forced-dissipative shallow water turbulence on the sphere
Although possibly the simplest model for the atmospheres of the giant planets, the turbulent forceddissipative shallow-water system in spherical geometry has not, to date, been investigated; the… Expand
The Importance of the Nontraditional Coriolis Terms in Large-Scale Motions in the Tropics Forced by Prescribed Cumulus Heating
AbstractIn meteorological dynamics, the shallow-atmosphere approximation is generally used in the momentum equation, together with the “traditional approximation.” In the traditional approximation,… Expand
An oceanic general circulation model framed in hybrid isopycnic-Cartesian coordinates
TLDR
The intent of this approach, some of whose features are reminiscent of the Arbitrary Lagrangian–Eulerian (ALE) technique, is to combine the best features of isopycnic-coordinate and fixed-grid circulation models within a single framework. Expand
The Stability of Short Symmetric Internal Waves on Sloping Fronts: Beyond the Traditional Approximation
AbstractThe interaction of internal waves with geostrophic flows is found to be strongly dependent upon the background stratification. Under the traditional approximation of neglecting the horizontal… Expand
Nonlinear dynamics of rotating shallow water : methods and advances
The rotating shallow water (RSW) model is of wide use as a conceptual tool in geophysical fluid dynamics (GFD), because, in spite of its simplicity, it contains all essential ingredients of… Expand
Consistent approximate models of the global atmosphere: shallow, deep, hydrostatic, quasi-hydrostatic and non-hydrostatic
We study global atmosphere models that are at least as accurate as the hydrostatic primitive equations (HPEs), reviewing known results and reporting some new ones. The HPEs make spherical… Expand
...
1
2
3
4
...