Wave Damping Calculator

Water waves lose energy into bottom sediments when the water is relatively shallow. This applet allows the calculation of the damping rate for a wave in water of a given depth over an infinitely thick porous bottom layer. The bottom is characterised by a coefficient of permeability, K, with units of m^2.

The (spatial) damping rate is given as k_i; the damping of the wave amplitude proceeds exponentially, as **H(0)**exp(-k_i x), where **H(0)** is the initial height of the wave, and x is the propagation distance. The percentage loss of amplitude in one wave length is exp(-k_i L) and is given above, as **H(L)/H(0)**. The damping after travelling a distance, xd, is also given.

The porous media damping was first derived by Reid and Kaijura (1957) based on small values of the dimensionless permeability (s K/nu), where s is the wave angular frequency and nu is the kinematic viscosity of water, taken here as 2.6 x 10-6 m^2/s. There solution is also described in Chapter 9 of Dean and Dalrymple (1991). Liu and Dalrymple (1984), in a more elaborate treatment, show that the damping first increases with permeability as given by Reid and Kaijura and then decreases as predicted by Hunt (1959). It is the Reid and Kaijura solution that is used here.

References:

Dean, R.G. and R.A. Dalrymple, **Water Wave Mechanics for Engineering and Scientists,** World Scientific Press, 1991.

Liu, P.L.-F. and R.A. Dalrymple, The damping of Gravity Water-Waves Due to Percolation, Coastal Engineering, 8, 33-49, 1984.

Reid, R.O. and K. Kaijura, On the Damping of Gravity Waves over a Permeable Seabed,
Trans. Amer. Geophys. Union, 38, 1957.

Problem: Show by example that wave/soil combinations that have the same dimensionless permeability have the same damping.

Comments: Robert Dalrymple