Seiching is the formation of standing waves in water body, due to wave formation and subsequent reflections from the ends. These waves may be incited by earthquake motions (similar to the motions caused by shaking a glass of water), impulsive winds over the surface, or due to wave motions entering the basin. The various modes of seiching correspond to the natural frequency reponse of the water body.

In this example, a rectangular basin (of infinite width) with given length and depth is seiching in accordance with the mode that you specified (greater than zero). The period of seiching (*T*) is determined by finding the correct length wave that will fit in the basin for the given water depth (based on linear water wave theory). The percent refers to the difference between the seiching period predicted by the dispersion relationship versus that usually used: shallow water theory.

(For shallow water theory, the seiching period is given by twice the basin length (*l*) divided by the modal number (*n*) and the speed of a shallow water wave (which depends on the water depth *h*):
)

As an example, try a basin of length 100 m, a depth of 20 m, and a mode number of two. Note that the water surface motion is out of phase with the velocities (shown with white lines). Also notice that the water motions do not have the elliptical orbits as progressive waves do (as in the Linear Kinematics applet). Under a node (no displacement of the water surface), the velocity is always horizontal, while under an antinode (max. displacement), the velocity is vertical. Further, this example (with quite a large water depth) gives quite a discrepancy between the linear theory result of the applet and the shallow water theory.

In the figure, you will notice that the number of modes corresponds to the number of nodal points (points of no motion of the water surface).

There are an infinite number of seiching modes possible, from the lowest (mode 1) to infinity. The period of oscillation decreases with mode number. Realistically, the lower modes probably occur in nature, as frictional damping affects the higher modes preferentially (higher frequency).

The seiching calculations for linear theory are given in Chapter 4 and 5 of Dean and Dalrymple, **Water Wave Mechanics for Engineers and Scientists,** World Scientific Press.)

Comments: Robert Dalrymple

Center for Applied Coastal Research

University of Delaware, Newark DE 19716

USA