FUNDAMENTAL PROPERTIES OF BOUSSINESQ-TYPE EQUATIONS FOR WAVE MOTION OVER A PERMEABLE BED.

This paper presents analyses of the fundamental properties of the fully nonlinear Boussinesq-type equations for waves and currents over a permeable seabed introduced by Chen [2005]. These properties are the wave celerity and the spatial porous damping rate for wave propagation on permeable beds. The governing equations for horizontally two-dimensional wave and current motions are first summarized, citing its methods of derivation, applicability and accuracy, and with emphasis on the inclusion of higher-order dispersive damping terms in the permeable-layer momentum equation. Then the fundamental properties are analyzed by extracting the complex linear dispersion relation embedded in the model equations using a Stokes-type approach and accounting for the coupling of the real and imaginary wavenumbers. Plots of the fundamental properties reveal that the inclusion of higher-order dispersive damping terms in the porous-layer momentum equation improves its agreement with the exact solution from shallow to deep water. Inclusion of these terms is also indispensable in obtaining accurate fundamental properties for high values of the permeable-layer thickness ratio. Determination of the model parameter values based on optimization is discussed. Finally, rational expansion of the dispersion equations is used to elucidate the observed behavior of the model's fundamental properties. [ABSTRACT FROM AUTHOR]