NOTES AND CORRESPONDENCE Constituent Boussinesq Equations for Waves and Currents

Abstract

The Boussinesq long-wave equations in constituent form are generalized to encompass both the irrotational long-wave dynamics and the rotational current dynamics. For irrotational long waves, the generalized equations are shown to represent both the weakly nonlinear and fully nonlinear Boussinesq-type wave equations given previously in the literature. The generalized equations are of additional interest in that they are effectively model equations for a weakly nonhydrostatic wave/current system, in which the conventional hydrostatic ocean current/wave model is a limiting case. The derived equations are related to the surface flow variables that are accessible to synoptic surface wave/current measurements such as those available from radar remote sensing.