A Quasi-Eulerian, Quasi-Lagrangian View of Surface-Wave-Induced Flow in the Ocean

In this study the influence of surface waves on the mean flow in an ocean of arbitrary depth is examined. The wave-induced forcing on the mean flow is obtained by integrating the Eulerian equations for mass and momentum balance from the bottom to an undulating material surface within the water column. By using the mean position of the material surface as the vertical coordinate, the authors obtain the depth dependence of the mean flow and the wave-induced forcing. Substitution of the vertical coordinate makes the model Lagrangian in the vertical direction. The model is Eulerian in the horizontal direction, allowing one to model the effects of a spatially nonuniform wave field or varying depth in a straightforward way.

NON-UNIFORM ALONGSHORE CURRENTS

Alongshore gradients of breaker height have been shown to significantly influence the velocities and circulation patterns of nearshore current systems. Experimental data from an idealized laboratory experiment shows that the form of the nonuniform wave generated current system resulting from diffraction behind an offshore breakwater is essentially determined by the beach-breakwater geometry while its magnitude depends upon the wave height. Furthermore the current may produce significant increases in the magnitude of the wave set-up within the three dimensional system. For the case investigated, where the alongshore gradient of breaker height is comparatively large, the maximum mean alongshore current velocity is not greatly affected by bottom resistance and may be computed for plunging breakers from a relation of the following form.

EFFECTS OF NONUNIFORM WAVE ENERGY IN THE LITTORAL ZONE

Bi-weekly monitoring of four closely-spaced permanent beach profile stations located on the northeast end of Monomoy Island (Cape Cod) has revealed major variations in the amount of erosion and accretion occurring along this portion of the Massachusetts shoreline During the 27-month monitoring period a close relationship was observed between changes in the beach and offshore portions of the profiles Three distinct types of bars were noted (1) Subtidal bars which are parallel to the shoreline and located one to two thousand feet off those portions of the shoreline undergoing relatively small amounts of beach erosion, (2) Subtidal bars which are perpendicular to the shoreline and attached to areas of the shore undergoing large amounts of erosion, and (3) Large intertidal bars which are oriented obliquely to the shoreline and associated with the formation of the ebb-tidal delta and the resulting wave refraction patterns The large variations in erosion and accretion occurring along the beach at any one time are related to the nonumform distribution of energy within the waves arriving at this section of the coastline This nonunifortuity of wave energy is attributed to refraction of the waves around the irregular bathymetry offshore from Monomoy, and it appears to produce shoreline protuberances of sand which are flanked updrift and downdrift by erosional zones.