[1] Based on a literature overview, this paper summarizes the impact and legacy of the contributions of Wilfried Brutsaert and Jean-Yves Parlange (Cornell University) with respect to the current state-of-the-art understanding in hydraulic groundwater theory. Forming the basis of many applications in catchment hydrology, ranging from drought flow analysis to surface water-groundwater interaction...

Simulations of nonlinear, anelastic convection in the presence of magnetic fields have revealed a complex array of dynamic phenomena, including several kinds of nonlinear oscillations (Lantz & Sudan 1993). In an attempt to identify the physical mechanism responsible for these oscillations, a simple model is proposed in which the full magnetoanelastic equations are replaced by equations for the ...

Abstract Many of the widely used models for description nonlinear surface gravity waves, in deep or shallow water, such as High Order Spectral Method (HOSM) and Boussinesq-type equations, rely on elimination vertical coordinate from basic three-dimensional Euler equations. From a numerical point view are often computationally efficient, which is one main reasons that many frequently studies wav...

In this paper, we study various dissipative mechanics associated with the Boussinesq systems which model two-dimensional small amplitude long wavelength water waves. We will show that the decay rate for the damped one-directional model equations, such as the KdV and BBM equations, holds for some of the damped Boussinesq systems.

The 2D incompressible Boussinesq system with partial or fractional dissipation have recently attracted considerable attention. In this paper, we study the Cauchy problem for the 2D Boussinesq system in a periodic domain with fractional vertical dissipation in the subcritical case, and we prove the global well-posedness of strong solutions. Based on this, we also discuss the existence of the glo...

We offer a synthetic exposition on the state of art for Computational Fluid Dynamics (CFD) relevant to Navier–Stokes equations with Boussinesq approximation, smoothly blending history field an accessible underlying mathematical rationale, supporting theorems and survey landmark results subject. Attention is paid those efforts which have opened up new paradigms in modern CFD, techniques that eme...

the assumptions considered in developing the saint-venant equations limit their application in many practical situations. the modified boussinesq equation was presented to overcome the limitation imposed by saint-venant equation due to the presence of non-hydrostatic pressure distribution and steep slope. in this paper a computational model was developed for solving the modified and the traditi...

subsurface drainage systems are used to control the depth of the water table and to reduce or prevent soil salinity. water flow in these systems is described by the boussinesq equation, and the advection-dispersion equation coupled with the boussinesq equation is used to study the solute transport. the objective of this study was to propose a finite difference solution of the advection-dispersi...

The influence of gas bubbles on the properties of internal waves in a continuously stratified fluid is studied in the framework of a two-dimensional model of a diluted monodisperse mixture of an incompressible fluid with gas bubbles. The model takes into account surface tension on the walls of the bubbles and an effective viscosity. The dispersion relation is obtained for linear waves in the Bo...