It is well known that the Boussinesq equation is the bidirectional equivalent of the celebrated Korteweg-de Vries equation. Here we consider Boussinesq-type versions of two classical unidirectional integrable equations. A procedure is presented for deriving multisoliton solutions of one of these equations – a bidirectional Kaup–Kupershmidt equation. These solitons have the unusual property that...

A novel parallel technique for Fourier-Galerkin pseudo-spectral methods with applications to two-dimensional Navier-Stokes equations and inviscid Boussinesq approximation equations is presented. It takes the advantage of the programming structure of the phase-shift de-aliased scheme for pseudo-spectral codes, and combines the task-distribution strategy [Yin, Clercx and Montgomery, Comput. Fluid...

A Boussinesq-type wave model is developed to numerically investigate the breaking waves and wave-induced currents. All the nonlinear terms are retained in the governing equations to keep fully nonlinearity characteristics and it hence more suitable to describe breaking waves with strong nonlinearity in the nearshore region. The Boussinesq equations are firstly extended to incorporate wave break...

Thin liquid films are ubiquitous in nature and have many practical applications. From biological to the curtain coating process, thin present both large small scales. Despite their importance, understanding stability of these remains a significant challenge due fluid–fluid interface that is free deform, affected by interfacial tension complex rheological behavior. Instabilities often caused van...

This paper describes the numerical model BOUSS-WMH (BOUSSinesq Wave Model for Harbours), a finite element model for nonlinear wave propagation near shore and into harbors. It is based upon an extended version of the Boussinesq equations to which terms were added to generate regular or irregular waves inside the numerical domain, absorb outgoing waves, partially reflect waves at physical boundar...

Measurements of the Nusselt number N as a function of the Rayleigh number R using ethane gas near its critical point show that N is enhanced by non-Oberbeck-Boussinesq (NOB) effects when the top temperature approaches the coexistence curve. The empirical criterion that a small ∆ρ/ρ (ρ is the density) implies Boussinesq behavior is found not to be valid. An examination of data by Chavanne et al....

A variational framework is defined for vertical slice models with three-dimensional velocity depending only on x and z. The models that result from this framework are Hamiltonian, and have a Kelvin– Noether circulation theorem that results in a conserved potential vorticity in the slice geometry. These results are demonstrated for the incompressible Euler– Boussinesq equations with a constant t...

We construct new integrable coupled systems of N = 1 supersymmetric equations and present integrable fermionic extensions of the Burgers and Boussinesq equations. Existence of infinitely many higher symmetries is demonstrated by the presence of recursion operators. Various algebraic methods are applied to the analysis of symmetries, conservation laws, recursion operators, and Hamiltonian struct...

The objective of this paper is to propose a hyperbolic relaxation technique for the dispersive Serre-Green-Naghdi equations (also known as fully non-linear Boussinesq equations) with full topography effects introduced in Green, A.E. and Naghdi, P.M. (J. Fluid Mech., 78, 237-246, 1976) Seabra-Santos el al Mec.h, 176, 117-134, 1997). This done by revisiting similar Guermond Comput. Phys., 399, 10...

The modulational stability of both the Korteweg-de Vries (KdV) and the Boussinesq wavetralns is investigated using Whltham’s variational method. It is shown that both KdV and Boussinesq wavetrains are modulationally stable. This result seems to confirm why it is possible to transform the KdV equation into a nonlinear Schr’dinger equation with a repulsive potential. A brief discussion of Whltham...