相关论文: Shallow Water Memory: Stokes and Darwin Drifts

We introduce a physically relevant stochastic representation of the rotating shallow water equations. The derivation relies mainly on a stochastic transport principle and on a decomposition of the fluid flow into a large-scale component and…

A quasi-second order scheme is developed to obtain approximate solutions of the shallow water equationswith bathymetry. The scheme is based on a staggered finite volume scheme for the space discretization:the scalar unknowns are located in…

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…

The free graviton theory given by linearising Einstein's theory has a dual formulation in terms of a dual graviton field. The dual graviton theory has two gauge invariances giving rise to two conserved charges, while the ADM charges of the…

The Euler's equations describe the motion of inviscid fluid. In the case of shallow water, when a perturbative asymtotic expansion of the Euler's equations is taken (to a certain order of smallness of the scale parameters), relations to…

Shallow water equations (SWE) are fundamental nonlinear hyperbolic PDE-based models in fluid dynamics that are essential for studying a wide range of geophysical and engineering phenomena. Therefore, stable and accurate numerical methods…

This work extends the proof of a local version of the linearized second law involving an entropy current with non-negative divergence by including the arbitrary non-minimal coupling of scalar and $U(1)$ gauge fields with gravity. In recent…

Over the past few decades, a host of theoretical evidence have surfaced that suggest a connection between theories of gravity and Navier-Stokes (NS) equation of fluid dynamics. It emerges out that gravity theory can be treated as some kind…

The purpose of this paper is to derive rigorously the so called viscous shallow water equations given for instance page 958-959 in [A. Oron, S.H. Davis, S.G. Bankoff, Rev. Mod. Phys, 69 (1997), 931?980]. Such a system of equations is…

Particles in turbulence live complicated lives. It is nonetheless sometimes possible to find order in this complexity. It was proposed in [Falkovich et al., Phys. Rev. Lett. 110, 214502 (2013)] that pairs of Lagrangian tracers at small…

We extend the formalism of the statistical theory developed for the 2D Euler equation to the case of shallow water system. Relaxation equations towards the maximum entropy state are proposed, which provide a parametrization of sub-grid…

We study a possibly integrable model of abelian gauge fields on a two-dimensional surface M, with volume form mu. It has the same phase space as ideal hydrodynamics, a coadjoint orbit of the volume-preserving diffeomorphism group of M,…

We study the second derivative effects on the constitutive relations of an uncharged parity-even Galilean fluid using the null fluid framework. Null fluids are an equivalent representation of Galilean fluids in terms of a higher dimensional…

In this paper, we reformulate the Schrodinger equation in gauge-theoretic terms. Starting from the Madelung representation, we rewrite the conserved probability-current using gauge fields, namely a one-form gauge field in the…

The anelastic and pseudo-incompressible equations are two well-known soundproof approximations of compressible flows useful for both theoretical and numerical analysis in meteorology, atmospheric science, and ocean studies. In this paper,…

An overview is presented of several diverse branches of work in the area of effectively 2D fluid equilibria which have in common that they are constrained by an infinite number of conservation laws. Broad concepts, and the enormous variety…

The two-dimensional (2-D) Euler equations of a perfect fluid possess a beautiful geometric description: they are reduced geodesic equations on the infinite-dimensional Lie group of symplectomorphims with respect to a right-invariant…

This talk gives an overview of the recently-formulated Fluid/Gravity correspondence, which was developed in the context of gauge/gravity duality. Mathematically, it posits that Einstein's equations (with negative cosmological constant) in…

The gauge covariant derivative of a wave function is ubiquitous in gauge theory, and with associated gauge transformations it defines charged currents interacting with external fields, such as the Lorentz force exerted by an electromagnetic…

Using gauge theory /string theory correspondence certain universal aspects of the strongly coupled four dimensional gauge theory hydrodynamics were established in hep-th/0311175. The analysis were performed in the framework of ``membrane…