On the Damping of Second-Class Trapped Waves on a Sloping Beach

Abstract

The effect of linear bottom friction on free topographic (second class) waves on a sloping beach is investigated. To handle the coastal singularity in the friction terms, Lighthill's method of strained coordinates is used to find a perturbation solution to the governing equations. Simple expressions for the decay rate are worked out for two classical beach profiles: 1) the uniformly sloping beach, and 2) the exponential depth profile due to Ball (1967). For parameter values characteristic of the north shore of Lake Ontario, which can be modelled by the Ball profile, only the gravest mode will not experience rapid attenuation due to bottom friction.