A family of Boussinesq systems has recently been proposed by Bona, Chen, and Saut in [J.L. Bona, M. Chen, J.-C. Saut, Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media. I. Derivation and linear theory, J. Nonlinear Sci. 12 (4) (2002) 283–318] to describe the two-way propagation of small-amplitude gravity waves on the surface of water in a canal....

For flows with small density variations, it is convenient to approximate them as incompressible whilst retaining the leading order effects due to the density variations, thus avoiding issues associated with acoustic waves. The classical approach is the Boussinesq approximation which was originally motivated by the desire to account for gravitational buoyancy effects. There are many situations o...

Intermediate-depth, Boussinesq-type modelling is used to generalize previously known results for surface water waves propagating over arbitrarily shaped topographies. The improved reduced wave model is obtained after studying how small changes in the linear dispersion relation (over a flat bottom) can become dramatically important in the presence of a highly fluctuating topography. Numerical va...

This paper describes a σ -coordinate scalar transport model coupled with a Boussinesq-type hydrodynamic model. The Boussinesq model has the ability to calculate both three-dimensional velocity distributions and the water surface motion. To capture ‘dispersion’ processes in open channel flow, horizontal vorticity effects induced by a bottom shear stress are included in the Boussinesq model. Thus...

The simplifications required to apply the Boussinesq approximation to compressible flow are compared with those in an incompressible fluid. The larger degree of approximation required to describe mass conservation in a stratified compressible fluid with the Boussinesq continuity equation has led to the development of several different sets of “anelastic” equations that may be regarded as genera...

An improved curvilinear grid model based on fully nonlinear Boussinesq equations is used to simulate wave propagation in Ponce de Leon Inlet, Fla. We employ the nearshore bathymetry of Ponce de Leon Inlet and generate a stretched curvilinear grid that can resolve shortwaves in the nearshore region and fit the complex geometry. Simulations of 18 cases with monochromatic input waves and Texel-Mar...

this paper presents an analytical model characterizing unsteady groundwater flow in an unconfined aquifer resting on a sloping impervious bed. the aquifer is in contact with a constant water level at one end. the other end is connected to a stream whose level is increasing form an initial level to a final level at a known exponentially decaying function of time. moreover, the aquifer is repleni...

While non-Boussinesq hexagonal convection patterns are well known to be stable close to threshold (i.e. for Rayleigh numbers R ≈ Rc), it has often been assumed that they are always unstable to rolls already for slightly higher Rayleigh numbers. Using the incompressible Navier-Stokes equations for parameters corresponding to water as a working fluid, we perform full numerical stability analyses ...

Depth-integrated long-wave models, such as the shallow-water and Boussinesq equations, are standard fare in the study of small amplitude surface waves in shallow water. While the shallow-water theory features conservation of mass, momentum and energy for smooth solutions, mechanical balance equations are not widely used in Boussinesq scaling, and it appears that the expressions for many of thes...