A derivation of equations for wave propagation in water of variable depth

Within the scope of the three-dimensional theory of homogeneous incompressible inviscid fluids, this paper contains a derivation of a system of equations for propagation of waves in water of variable depth. The derivation is effected by means of the incompressibility condition, the energy equation, the invariance requirements under superposed rigid-body motions, together with a single approximation for the (three-dimensional) velocity field.

[1]  P. M. Naghdi,et al.  The Theory of Shells and Plates , 1973 .

[2]  P. M. Naghdi,et al.  Directed fluid sheets , 1976, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[3]  D. Peregrine.  Long waves on a beach , 1967, Journal of Fluid Mechanics.

[4]  D. Peregrine.  Equations for Water Waves and the Approximation behind Them , 1972 .

[5]  R. Johnson.  On the development of a solitary wave moving over an uneven bottom , 1973, Mathematical Proceedings of the Cambridge Philosophical Society.

[6]  P. M. Naghdi,et al.  On the theory of water waves , 1974, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[7]  Roger H.J. Grimshaw,et al.  The solitary wave in water of variable depth , 1970, Journal of Fluid Mechanics.