Bidimensional shallow water model with polynomial dependence on depth through vorticity

Interaction of surface waves with vorticity in shallow water.

Vortical flows in shallow water interact with long surface waves by virtue of the nonlinear terms of the fluid equations. Analytical formulae are derived that quantify the spontaneous generation of such waves by unsteady vorticity as well as the scattering of surface waves by vorticity. In a first Born approximation the radiated surface elevation is linearly related to the Fourier transform of ...

Simulation of a viscous fluid spreading by a bidimensional shallow water model

In this paper we propose a numerical method to solve the Cauchy problem based on the viscous shallow water equations in an horizontally moving domain. More precisely, we are interested in a flooding and drying model, used to modelize the overflow of a river or the intrusion of a tsunami on ground. We use a non conservative form of the two-dimensional shallow water equations, in eight velocity f...

Polarization lidar for shallow water depth measurement.

A bathymetric, polarization lidar system transmitting at 532 nm and using a single photomultiplier tube is employed for applications of shallow water depth measurement. The technique exploits polarization attributes of the probed water body to isolate surface and floor returns, enabling constant fraction detection schemes to determine depth. The minimum resolvable water depth is no longer dicta...

Bidimensional -stable Models with Long-range Dependence

In this paper, we propose an -stable 2D extension of the 1D fractional Gaussian noise. The considered model exhibits long-range dependence properties, while its stability index allows us to control the degree of spikyness of the synthesized fields. A least square method for the estimation of the three parameters of this model is also described and its performances are evaluated by a Monte Carlo...

A nonlinear Schrödinger equation for water waves on finite depth with constant vorticity