The wave height variation for regular waves in shoaling water

Abstract

The theory of cnoidal wave shoaling has previously been connected to data in deeper water (described by sinusoidal wave theory) by assuming continuity in energy flux E f at the matching point between the two theories (Svendsen and Brink-Kjær, 1972) resulting in a small shift in wave height H at the matching point. In this paper we assume directly continuity in wave height and tables are given from which the wave height variation can be determined when the wave is specified at any water depth (including deep water). It is also shown that a deep water limit for cnoidal waves exists. The nature of this limit and the behaviour of the waves close to it are analysed. Experimental data for waves with no free second harmonic components are compared with a shoaling model based on linear theory for h/L 0 > 0.10 and cnoidal theory for h/L 0 < 0.10 . The agreement is very good for deep water wave steepnesses H 0 /L 0 up to 3–4%. For larger steepnesses the linear theory fails to predict the variation for h/L 0 > 0.10 .