Related papers: A Gauge Theory for Shallow Water

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…

The classical system of shallow-water (Saint--Venant) equations describes long surface waves in an inviscid incompressible fluid of a variable depth. Although shock waves are expected in this quasilinear hyperbolic system for a wide class…

The classical theory of non-relativistic charged particle interacting with U(1) gauge field is reformulated as the Schr\"odinger wave equation modified by the de-Broglie-Bohm quantum potential nonlinearity. For, (1 - $\hbar^2$) deformed…

A basic shallow water system with variable topography is analyzed from the point of view of a Lagrangian derivation of momentum, energy, and pseudomomentum balances. A two-dimensional action and associated momentum equation are derived. The…

When traditional linearised theory is used to study gravity-capillary waves produced by flow past an obstruction, the geometry of the object is assumed to be small in one or several of its dimensions. In order to preserve the nonlinear…

The purpose of this article is to clarify the Cauchy theory of the water waves equations as well in terms of regularity indexes for the initial conditions as for the smoothness of the bottom of the domain (namely no regularity assumption is…

We show that interfacial gravity waves comprising strong hydraulic jumps (bores) can be described by a two-layer hydrostatic shallow-water (SW) approximation without invoking additional front conditions. The theory is based on a new SW…

Formally second-order correct, mathematical descriptions of long-crested water waves propagating mainly in one direction are derived. These equations are analogous to the first-order approximations of KdV- or BBM-type. The advantage of…

The system of equations of one-dimensional shallow water over uneven bottom in Euler's and Lagrange's variables is considered. Intermediate system of equations is introduced. Hydrodynamic conservation laws of intermediate system of…

A statistical method for calculating equilibrium solutions of the shallow water equations, a model of essentially 2-d fluid flow with a free surface, is described. The model contains a competing acoustic turbulent {\it direct} energy…

Chern-Simons gauge theory, since its inception as a topological quantum field theory, has proved to be a rich source of understanding for knot invariants. In this work the theory is used to explore the definition of the expectation value of…

We propose a symmetry law for a doublet of different form fields, which resembles gauge transformations for matter fields. This may be done for general Lie groups, resulting in an extension of Lie algebras and group manifolds. It is also…

Topological gauge theories describe the low-energy properties of certain strongly correlated quantum systems through effective weakly interacting models. A prime example is the Chern-Simons theory of fractional quantum Hall states, where…

We examine Chern-Simons theory as a deformation of a 3-dimensional BF theory that is partially holomorphic and partially topological. In particular, we introduce a novel gauge that leads naturally to a one-loop exact quantization of this BF…

The shear viscosity is a fundamental transport property of matter. Here we derive a general theory of the viscosity of gases based on the relativistic Langevin equation (deduced from a relativistic Lagrangian) and nonaffine linear response…

Though a Chern-Simons (2k-1)-form is not gauge-invariant and it depends on a background connection, this form seen as a Lagrangian of gauge theory on a (2k-1)-dimensional manifold leads to the energy-momentum conservation law.

The problem of interest in this article are waves on a layer of finite depth governed by the Euler equations in the presence of gravity, surface tension, and vertical electric fields. Perturbation theory is used to identify canonical…

Long waves in shallow water propagating over a background shear flow towards a sloping beach are being investigated. The classical shallow-water equations are extended to incorporate both a background shear flow and a linear beach profile,…

In the paper a new nonlinear equation describing shallow water waves with the topography of the bottom directly taken into account is derived. This equation is valid in the weakly nonlinear, dispersive and long wavelength limit. Some…

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…