Related papers: Shallow water equations on a fast rotating surface
The present work is devoted to the derivation of a fully well-balanced and positivepreserving numerical scheme for the shallow water equations with Coriolis force. The first main issue consists in preserving all the steady states, including…
A formulation of the shallow water equations adapted to general complex terrains is proposed. Its derivation starts from the observation that the typical approach of depth integrating the Navier-Stokes equations along the direction of…
Using nonstandard methods, we show that the time dependent Fourier series of any smooth function F, solving the wave equation, on a finite closed interval, with vanishing boundary conditions, converges uniformly to F.
In this article we consider the inviscid two-dimensional shallow water equations in a rectangle. The flow occurs near a stationary solution in the so called supercritical regime and we establish short term existence of smooth solutions for…
In this note, we announce a complete classification of stability of periodic roll-wave solutions of the viscous shallow-water equations, from their onset at Froude number $F\approx 2$ up to the infinite-Froude limit. For intermediate Froude…
This paper extends the analytical study of the incompressible Euler equations from the classical spherical setting to the more realistic geometry of a biaxial ellipsoid. Motivated by the work of Cheng and Mahalov on fast rotating spheres…
We perform a detailed Lie symmetry analysis for the hyperbolic system of partial differential equations that describe the one-dimensional Shallow Water magnetohydrodynamics equations within a rotating reference frame. We consider a relaxing…
We numerically analyse the rotation of a neutrally buoyant spheroid in a shear flow at small shear Reynolds number. Using direct numerical stability analysis of the coupled nonlinear particle-flow problem we compute the linear stability of…
This study analyzes steady periodic hydroelastic waves propagating on the water surface of finite depth beneath nonlinear elastic membranes. Unlike previous work \cite{BaldiT,BaldiT1,Toland,Toland1}, our formulation accommodates rotational…
We prove that the flow map associated to a model equation for surface waves of moderate amplitude in shallow water is not uniformly continuous in the Sobolev space $H^s$ with $s>3/2$. The main idea is to consider two suitable sequences of…
Geophysical flows are characterized by rapid rotation. Simulating these flows requires small timesteps to achieve stability and accuracy. Numerical stability can be greatly improved by the implicit integration of the terms that are most…
We present two accurate and efficient algorithms for solving the incompressible, irrotational Euler equations with a free surface in two dimensions with background flow over a periodic, multiply-connected fluid domain that includes…
We study 2D Euler equations on a rotating surface, subject to the effect of the Coriolis force, with an emphasis on surfaces of revolution. We bring in conservation laws that yield long time estimates on solutions to the Euler equation, and…
We prove the persistence of boundary smoothness of vortex patches for the quasi-geostrophic shallow-water (QGSW) equations. The QGSW equations generalize the Euler equations by including an additional parameter, the Rossby radius…
We give a simple proof for the rotational symmetry of ancient solutions of Ricci flow on surfaces. As a consequence we obtain a simple proof of some results of P.Daskalopoulos, R.Hamilton and N.Sesum on the a priori estimates for the…
In this paper we derive a new formulation of the water waves equations with vorticity that generalizes the well-known Zalkarov-Craig-Sulem formulation used in the irrotational case. We prove the local well-posedness of this formulation, and…
How anisotropic particles rotate and orient in a flow depends on the hydrodynamic torque they experience. Here we compute the torque acting on a small spheroid in a uniform flow by numerically solving the Navier-Stokes equations. Particle…
We consider the rotation of small neutrally buoyant axisymmetric particles in a viscous steady shear flow. When inertial effects are negligible the problem exhibits infinitely many periodic solutions, the "Jeffery orbits". We compute how…
This work is devoted to the study of a viscous shallow-water system with friction and capillarity term. We prove in this paper the existence of global strong solutions for this system with some choice of large initial data when $N\geq 2$ in…
We study periodic, two-dimensional, gravity-capillary traveling wave solutions to a viscous shallow water system posed on an inclined plane. While thinking of the Reynolds and Bond numbers as fixed and finite, we vary the speed of the…