We apply a multiple–time version of the reductive perturbation method to study long waves as governed by the Boussinesq model equation. By requiring the absence of secular producing terms in each order of the perturbative scheme, we show that the solitary–wave of the Boussinesq equation can be written as a solitary–wave satisfying simultaneously all equations of the KdV hierarchy, each one in a...

We study asymptotic behavior of the global attractors to the Boussinesq system for Rayleigh-B enard convection at large Prandtl number. In particular, we show that the global attractors to the Boussinesq system for Rayleigh-B enard convection converge to that of the in nite Prandtl number model for convection as the Prandtl number approaches in nity. This o ers partial justi cation of the in ni...

the spontaneous generation of inertia–gravity waves (igws) in the idealized simulation of vortical flows is investigated using the isentropic two-layer model on a sphere. the contour-advective semi-lagrangian (casl) algorithm is applied to solve the primitive equations using the potential vorticity (pv), velocity divergence, and acceleration divergence as the prognostic variables. the casl algo...

In this paper, a systematic, overall view of theories for periodic waves of permanent form, such as Stokes and cnoidal waves, is described first with their validity ranges. To deal with random waves, a method for estimating directional spectra is given. Then, various wave equations are introduced according to the assumptions included in their derivations. The mild-slope equation is derived for ...

We consider the three-dimensional Boussinesq equations, and obtain an Osgood type regularity criterion in terms of the velocity gradient.

We propose a novel approach for bridging the Boussinesq equations and the primitive equations. This approach uses spatio-temporal filtering as an alternative to traditional scaling arguments. © 2009 Elsevier Ltd. All rights reserved.

In this paper, we propose the extended Boussinesq–Whitham–Broer–Kaup (BWBK)-type equations with variable coefficients and fractional order. We consider BWBK equations, Whitham–Broer–Kaup (WBK) Boussinesq by setting proper smooth functions that are derived from proposed equation. obtain uniformly coupled traveling wave solutions of considered employing improved system method, subsequently their ...

In a previous study [DD07b] we presented a novel visco-potential free surface flows formulation. The governing equations contain local and nonlocal dissipative terms. From physical point of view, local dissipation terms come from molecular viscosity but in practical computations, rather eddy viscosity should be used. On the other hand, nonlocal dissipative term represents a correction due to th...