The effect of a sudden change of bottom topography on tides. A wave approaching a step-like depth change from the deep water (h1) side is partly reflected at the step and continues partly as a propagating wave into the shallow water (h2) side.

The amplitude of the reflected wave is given by the reflection coefficient a, the amplitude of the wave which passes into shallow water by the transmission coefficient b.

Note that if the water depth is the same on both sides (h1 = h2) the wave passes without reflection (a = 0, b = 1). If h1 and h2 are different, we find b > 1; in other words, the amplitude is increased in shallow water. The reason for this is that the wave speed cdepends on the water depth as c = (gh)1/2. (g: gravity)

At a vertical wall (h2 = 0) the wave experiences total reflection (a = 1). For this wave we find b = 2, but this wave cannot propagate into the region of zero depth because its wave speed is zero.


© 1996 M. Tomczak

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