Study of Internal Wave Generation by Tide-Topography Interaction

Lecture by the Member Awarded the Okada Prize of the Oceanographical Society of Japan for 1989

Abstract

The generation mechanism of internal waves by a relatively strong tidal flow over a sill is clarified analytically. Special attention is directed to the role of the tidal advection effect, which is examined by use of characteristics.
An internal wave which propagates upstream is gradually formed through interference of infinitesimal amplitude internal waves (elementary waves) emanating from the sill at each instant of time. In the accelerating (or decelerating) stage of the tidal flow, the effective amplification of the internal wave takes place as the internal Froude number exceeds (or falls below) unity because during this period the internal wave slowly travels downstream (or upstream) while crossing over the sill where elementary wayes are efficiently superimposed. In fact, the variability in the internal wave field actually observed in a realistic situation (Stellwagen Bank in Massachusetts Bay) is shown to be satisfactorily interpreted in terms of this mechanism. Furthermore, by using this analytical model, the relation between the strength of the tidal advection effect and the resulting internal waveform is clarified.
This theory is easily extended to include a vertically sheared steady flow. In this case, although the fundamental generation mechanism is the same as above, the amplitude of the elementary wave varies with time depending on the relative direction of the tidal flow and steady shear flow, so that the internal wave field over the sill differs markedly between the ebb and flood tidal phases. As an example, the internal wave generation process over the sill in the Strait of Gibraltar is qualitatively discussed on the basis of this analytical model.
The effect of vertical mixing caused by breaking of these large-amplitude internal waves on the coastal environment is also pointed out. In particular, a brief discussion is made on the control of water exchange by the fortnightly modulation of tidal mixing processes at the sills and constrictions in channels connecting freshwater sources with the ocean.