A set of Boussinesq-type equations for interfacial internal waves in two-layer stratified fluid |
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Authors: | Song Jin-Bao |
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Institution: | Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China |
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Abstract: | Many new forms of Boussinesq-type equations have been developed to
extend the range of applicability of the classical Boussinesq
equations to deeper water in the study of the surface waves. One
approach was used by Nwogu (1993. J. Wtrw. Port Coastal and Oc. Eng.
119, 618--638) to improve the linear dispersion characteristics of
the classical Boussinesq equations by using the velocity at an
arbitrary level as the velocity variable in derived equations and
obtain a new form of Boussinesq-type equations, in which the
dispersion property can be optimized by choosing the velocity
variable at an adequate level. In this paper, a set of
Boussinesq-type equations describing the motions of the interfacial
waves propagating alone the interface between two homogeneous
incompressible and inviscid fluids of different densities with a
free surface and a variable water depth were derived using a method
similar to that used by Nwogu (1993. J. Wtrw. Port Coastal and Oc.
Eng. 119, 618--638) for surface waves. The equations were expressed
in terms of the displacements of free surface and density-interface,
and the velocity vectors at arbitrary vertical locations in the
upper layer and the lower layer (or depth-averaged velocity vector
across each layer) of a two-layer fluid. As expected, the equations
derived in the present work include as special cases those obtained
by Nwogu (1993, J. Wtrw. Port Coastal and Oc. Eng. 119, 618-638) and
Peregrine (1967, J. Fluid Mech. 27, 815-827) for surface waves when
the density of the upper fluid is taken as zero. |
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Keywords: | two-layer fluid interfacial
internal waves Boussinesq-type equations |
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