Boussinesq and non-Boussinesq gravity currents propagating on unbounded uniform slopes in the deceleration phase

Boussinesq Waves on Vertically Sheared Currents

Boussinesq modeling of longshore currents

[1] A time domain Boussinesq model for nearshore hydrodynamics is improved to obtain the conservation of vertical vorticity correct to second order and extended for use on an open coast using longshore periodic boundary conditions. The model is utilized to simulate surface waves and longshore currents under laboratory and field conditions. Satisfactory agreement is found between numerical resul...

On the Oberbeck-Boussinesq approximation on unbounded domains

We study the Oberbeck-Boussinesq approximation describing the motion of an incompressible, heat-conducting fluid occupying a general unbounded domain in R3. We provide a rigorous justification of the model by means of scale analysis of the full Navier-Stokes-Fourier system in the low Mach and Froude number regime on large domains, the diameter of which is proportional to the speed of sound. Fin...

Boussinesq Modeling of Alongshore Swash Zone Currents

The study involves theoretical formulation, model development and verification, and integration with field observations of swash motions. The starting point of the theoretical formulation is the Euler equation of motion for waves and currents above the permeable seabed and the locally-averaged Navier-Stokes equations for the flow inside the porous layer. A complete set of fully nonlinear Boussi...

Non-Planar Fronts in Boussinesq Reactive Flows

We consider the reactive Boussinesq equations in a slanted cylinder, with zero stress boundary conditions and arbitrary Rayleigh number. We show that the equations have non-planar traveling front solutions that propagate at a constant speed. We also establish uniform upper bounds on the burning rate and the flow velocity for general front-like initial data for the Cauchy problem.