Generation mechanism of internal waves by tidal flow over a sill

The generation mechanism of internal waves by 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 over the sill through the interference among infinitesimal amplitude internal waves (elementary waves) emanated from the sill at each instant of time. In the accelerating (decelerating) stage of tidal flow, the effective amplification of an internal wave takes place as the Froude number exceeds (falls below) unity, because during this period the internal wave slowly travels downstream (upstream), crossing over the sill, where elementary waves are efficiently superimposed. When the strength of the tidal advection effect is appropriate, the internal wave formed in the accelerating stage (Ac wave) and that formed in the decelerating stage (Dc wave) overlap, so that the resultant wave height becomes very large. Since the relative position of Ac and Dc waves varies depending on the strength of the tidal advection effect, the resultant internal wave form is strongly affected by it. When the tidal advection effect is strong, the Ac wave is carried too far downstream to interfere with the Dc wave, and hence the resultant wave form consists of two crests and two troughs. When the tidal advection effect is moderate, the optimum interference between Ac and Dc waves occurs, and the resultant wave form consists of one crest and one trough, with its horizontal scale approaching that of the sill. When the tidal advection effect is weak, the internal wave height becomes very small, since elementary waves propagate almost freely in the tidal flow without coming close together, and the resultant wave form approaches a sinusoidal wave of tidal frequency.