This paper is concerned with a two-dimensional Whitham–Boussinesq system modeling surface waves of an inviscid incompressible fluid layer. We prove that the associated Cauchy problem well-posed for initial data low regularity, existence time scale [Formula: see text], where text] and are small parameters related to level dispersion nonlinearity, respectively. In particular, in KdV regime text]}...

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 ...

A source function method for the generation of waves internal to Boussinesq model grid boundaries (Wei G, Kirby JT, Sinha A. Generation of waves in Boussinesq models using a source function method. Coastal Engng 1999;36:271–299) is generalized to account for the presence of a strong current, for application to wave-current interaction problems. The method is also modified to eliminate waves pro...

We prove the global well-posedness of the viscous incompressible Boussinesq equations in two spatial dimensions for general initial data in Hm with m ≥ 3. It is known that when both the velocity and the density equations have finite positive viscosity, the Boussinesq system does not develop finite time singularities. We consider here the challenging case when viscosity enters only in the veloci...

We numerically analyze Non-Oberbeck-Boussinesq (NOB) effects in two-dimensional Rayleigh-Bénard flow in glycerol, which shows a dramatic change in the viscosity with temperature. The results are presented both as functions of the Rayleigh number Ra up to 10 (for fixed temperature difference ∆ between the top and bottom plates) and as functions of ∆ (“nonOberbeck-Boussinesqness” or “NOBness”) up...

We examine the nature of the thermosolutal convection with or without rotation in the infinite Prandtl number regime, which is applicable to magma chambers. The onset of bifurcation and the structure of the bifurcated solutions in this double diffusion problem are analyzed. The stress-free boundary condition is imposed at the top and bottom plates confining the fluid. For the rotation free case...

A grid of numerical simulations of double-diffusive convection is presented for the astrophysical case where viscosity (Prandtl number Pr) and solute diffusivity (Lewis number Le) are much smaller than the thermal diffusivity. As in laboratory and geophysical cases convection takes place in a layered form. The proper translation between subsonic flows in a stellar interior and an incompressible...

Fringing reefs play an important role in protecting the coastal area by inducing wave breaking and wave energy dissipation. However, modeling of wave transformation and energy dissipation on this topography is still difficult due to the unique structure. In the present study, two-dimensional laboratory experiments were conducted to investigate the cross-shore variations of wave transformation, ...

The use of lattice gas (cellular automaton) models has recently been advocated as an interesting method for the simulat ion of fluid flow . Th ese automata are an idealizat ion of the real microscopic molecula r dynamics. We present a model derived from the hexagonal lat t ice gas ru les of Frisch Hasslacher and Pomea u (FHP) that incorporates buoyant forces and d iscusses its prope rt ies. We ...