The Propagation of Tsunamis

Summary The passage of a seismic sea‐wave, or tsunami, may be conveniently thought of in three stages:1 the development of the disturbance in the area of generation 2 the transmission across the ocean 3 the changes occurring near a sloping shore (usually referred to as the “run‐up” problem).The present paper deals with some of the hydrodynamical aspects of (2). Tsunamis are ordinarily recorded by tide‐gauges situated in harbours or estuaries. The record is therefore greatly complicated by reflexions, by seiches, and especially by the non‐linear effects induced by run‐up. An uncomplicated record should, following the theory of Jeffreys, show a “Jeffreys phase” at the beginning of the record, consisting of an exponential rise followed by an oscillatory portion; the record should be in the form of the graph of an Airy integral, and the first few swings of the marigram do in fact so correspond; for the tsunami of 1957, March 9 the interval between the first two maxima is in good agreement with theory. This Jeffreys phase passes continuously into a dispersive train, since it is only at the head of the tsunami that the “shallow water speed” ( gH )½ is applicable. This train, however, seems rapidly to be contaminated by the effects mentioned above, so that the dispersive train is then no longer obvious. The simple theory based on the concept of a non‐viscous incompressible liquid on a flat Earth needs further justification. It is shown that allowance for compressibility still leads to a Jeffreys phase, with only a small reduction in the velocity of propagation. These effects are of the order of one per cent, and a similar correction applies to internal waves. The effects of scouring of the ocean floor and of dissipation of energy by viscosity have been investigated for the passage of a tsunami across deep water. Both these effects are shown to be small.