Related papers: Comparison of variational balance models for the r…
Salmon's nearly geostrophic model for rotating shallow-water flow is derived in full spherical geometry. The model, which results upon constraining the velocity field to the height field in Hamilton's principle for rotating shallow-water…
The turbulent evolution of the shallow water system exhibits asymmetry in vorticity. This emergent phenomenon can be classified as "balanced", that is, it is not due to the inertial-gravity wave modes. The Quasi-Geostrophic (QG) system, the…
In this paper, we investigate the wave solutions of a stochastic rotating shallow water model. This approximate model provides an interesting simple description of the interplay between waves and random forcing ensuing either from the wind…
With a new unifying model for layered rotating shallow-water (RSW) and quasi-geostrophic (QG) equations, this paper sheds light on the relation between these two sets of equations. We propose here a new formulation of the quasi-geostrophic…
The rotating shallow water model is a simplification of oceanic and atmospheric general circulation models that are used in many applications such as surge prediction, tsunami tracking and ocean modelling. In this paper we introduce a class…
The shallow water equations provide a useful analogue of the fully compressible Euler equations since they have similar characteristics: conservation laws, inertia-gravity and Rossby waves and a (quasi-) balanced state. In order to obtain…
We review here the derivation of many of the most important models that appear in the literature (mainly in coastal oceanography) for the description of waves in shallow water. We show that these models can be obtained using various…
In analogy with similar effects in adiabatic compressible fluid dynamics, the effects of buoyancy gradients on incompressible stratified flows are said to be `thermal'. The thermal rotating shallow water (TRSW) model equations contain three…
Using nonlinear simulations in two settings, we demonstrate that QG$^\mathrm{+1}$, a potential-vorticity based next-order-in-Rossby balanced model, captures several aspects of ocean submesoscale physics. In forced-dissipative 3D simulations…
Stochastic partial differential equations have been used in a variety of contexts to model the evolution of uncertain dynamical systems. In recent years, their applications to geophysical fluid dynamics has increased massively. For a…
We study a nonlinear system of partial differential equations which describe rotating shallow water with an arbitrary constant polytropic index $\gamma $ for the fluid. In our analysis we apply the theory of symmetries for differential…
We give an exponentially-accurate normal form for a Lagrangian particle moving in a rotating shallow-water system in the semi-geostrophic limit, which describes the motion in the region of an exponentially-accurate slow manifold (a region…
Lie symmetry analysis is applied to study the nonlinear rotating shallow water equations. The 9-dimensional Lie algebra of point symmetries admitted by the model is found. It is shown that the rotating shallow water equations are related…
In this work, we study and extend a class of semi-Lagrangian exponential methods, which combine exponential time integration techniques, suitable for integrating stiff linear terms, with a semi-Lagrangian treatment of nonlinear advection…
The dynamics of large-scale geophysical fluids is primarily governed by the balance between the Coriolis force and the pressure gradient. This phenomenon, known as geostrophic equilibrium, is the basis for the geostrophic model, which has…
Semi-implicit time-stepping schemes for atmosphere and ocean models require elliptic solvers that work efficiently on modern supercomputers. This paper reports our study of the potential computational savings when using mixed precision…
In this paper, we consider a family of piecewise constant solutions of the quasi-geostrophic shallow-water (QGSW) equation. We derive the contour dynamics equation of the QGSW front, which is a nonlinear, nonlocal dispersive equation, and…
In this paper, high order well-balanced finite difference weighted essentially non-oscillatory methods to solve general systems of balance laws are presented. Two different families are introduced: while the methods in the first one…
We develop a well-balanced central-upwind scheme for rotating shallow water model with horizontal temperature and/or density gradients---the thermal rotating shallow water (TRSW). The scheme is designed using the flux globalization…
The high-order numerical solution of the non-linear shallow water equations (and of hyperbolic systems in general) is susceptible to unphysical Gibbs oscillations that form in the proximity of strong gradients. The solution to this problem…