Generation and dissipation of coastal internal tides

Abstract

Long surface waves passing over a depth discontinuity approximating the continental shelf can generate internal waves of significant amplitudes. In the ocean the internal waves are progressive with seaward components of both phase and group velocities. They form a wave beam whose vertical depth is twice the shelf depth and whose center aligns along the characteristic emanating from the surface above the shelf break. Coupling between the oceanic and shelf internal waves causes fine structure within the beam. The position and magnitude of the fine structure depends upon the geometric configuration of the continental shelf and the amount of friction present. As the beam propagates away from the shelf break, the more rapid spatial decay of the higher modes causes it to widen and take on a rounded form. Over the shelf, the internal motion is composed of one or two narrow beams. One emanates from the bottom of the shelf break and reflects back and forth between the surface and the bottom as it progresses up the shelf. The other, when it occurs, is its reflection from the coast which moves out across the shelf. For viscous cases, the reflected shelf beam is damped nearly completely before it returns to the shelf break. When the slope of the bottom is nowhere greater than that of the characteristics, no backward reflection occurs and the incident beam must be completely absorbed in the nearshore region. In the presence of friction, the sharp gradients of phase and amplitude found at the edges of the shelf and oceanic beams in the inviscid case have disappeared and the internal wave beams are widened.