A new seawater Boussinesq system is introduced, and it is shown that this approximation to the equations of motion of a compressible binary solution has an energy conservation law that is a consistent approximation to the Bernoulli equation of the full system. The seawater Boussinesq approximation simplifies the mass conservation equation to $ u 5 0, employs the nonlinear equation of state of s...

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...

We study here some asymptotic models for the propagation of internal and surface waves in a two-fluid system. We focus on the so-called long wave regime for one-dimensional waves, and consider the case of a flat bottom. Following the method presented in [6] for the one-layer case, we introduce a new family of symmetric hyperbolic models, that are equivalent to the classical Boussinesq/Boussines...

Howard's semi-circle theorem is generalized for three-dimensional disturbances in a non-Boussinesq stratified fluid with a mean flow varying horizontally and vertically. In case of Boussinesq approximation Howard's and Rayleigh's theorem are extended for three-dimensional disturbances in a fluid with a mean flow varying only with respect to the latitude.

The aim of this paper is to present a simplified, yet rigorous, deduction the Boussinesq approximated governing equations for buoyant flows. In order carry out core procedure, simplified version manifold asymptotic analyses available in literature discussed. method adopted study focussed on local balance valid general, not necessarily Newtonian, fluid. analysis carried by demonstrating leading ...

We rigorously establish that, in the long-wave regime characterized by the assumptions of long wavelength and small amplitude, bidirectional solutions of the improved Boussinesq equation tend to associated solutions of two uncoupled Camassa-Holm equations. We give a precise estimate for approximation errors in terms of two small positive parameters measuring the effects of nonlinearity and disp...

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...

Fully nonlinear extensions of Boussinesq equations are derived to simulate surface wave propagation in coastal regions. By using the velocity at a certain depth as a dependent variable (Nwogu 1993), the resulting equations have significantly improved linear dispersion properties in intermediate water depths when compared to standard Boussinesq approximations. Since no assumption of small nonlin...