相关论文: Extended shallow-water theories with thermodynamic…

We review the geometric structure of the IL$^0$PE model, a rotating shallow-water model with variable buoyancy, thus sometimes called ``thermal'' shallow-water model. We start by discussing the Euler--Poincar\'e equations for rigid body…

We rigorously justify the bilayer shallow-water system as an approximation to the hydrostatic Euler equations in situations where the flow is density-stratified with close-to-piecewise constant density profiles, and close-to-columnar…

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…

This paper investigates the geometric structure of a quasigeostrophic approximation to a recently introduced reduced-gravity thermal rotating shallow-water model that accounts for stratification. Specifically, it considers a low-frequency…

A scaling argument is presented that leads to a shallow water theory of non-axisymmetric disturbances in annular sections of thin Keplerian disks. To develop a theoretical construction that will aid in physically understanding the…

We derive general depth-integrated model equations for overland flows featuring the evolution of suspended sediment that may be eroded from or deposited onto the underlying topography ('morphodynamics'). The resulting equations include…

We study the properties of, and investigate the stability of a baroclinic zonal current in, a thermal rotating shallow-water model, sometimes called \emph{Ripa's model}, featuring stratification for quasigeostrophic upper-ocean dynamics.…

In this work, we develop a modelling framework for granular flows based on the shallow water moment equations on inclined planes. Under the assumption of a polynomial expansion of the velocity field, the model extends the classical shallow…

The purpose of this paper is to present a shallow-water-type model with multiple inhomogeneous layers featuring variable linear velocity vertical shear and startificaion in horizontal space and time. This is achieved by writing the layer…

Poincar\'e-gravity modes described by the shallow water equations in a rotating frame have non-trivial topology, providing a new perspective on the origin of equatorially trapped Kelvin and Yanai waves. We investigate the topology of…

We present a class of thermodynamic systems with constant thermodynamic curvature which, within the context of geometric approaches of thermodynamics, can be interpreted as constant thermodynamic interaction among their components. In…

A multiscale theory of interacting continuum mechanics and thermodynamics of mixtures of fluids, electrodynamics, polarization and magnetization is proposed. The mechanical (reversible) part of the theory is constructed in a purely…

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…

In the present work, we study the geometric structures of the Rotating Shallow Water Magnetohydrodynamics (RSW-MHD) equations through a Lie group invariant Euler-Poincar\'e variational principle. In this geometric framework, we derive new,…

We consider relativistic hydrodynamics in the limit where the number of spatial dimensions is very large. We show that under certain restrictions, the resulting equations of motion simplify significantly. Holographic theories in a large…

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…

We study the two-dimensional rotating shallow-water model describing Earth's oceanic layers. It is formally analogue to a Schr\"odinger equation where the tools from topological insulators are relevant. Once regularized at small scale by an…

In this paper, we investigate the two-dimensional extension of a recently introduced set of shallow water models based on a regularized moment expansion of the incompressible Navier-Stokes equations…

A reduced dynamical model is derived which describes the interaction of weak inertia-gravity waves with nonlinear vortical motion in the context of rotating shallow-water flow. The formal scaling assumptions are (i) that there is a…

The paper describes the unique geometric properties of ideal magnetohydrodynamics (MHD), and demonstrates how such features are inherited by extended MHD, viz. models that incorporate two-fluid effects (the Hall term and electron inertia).…