On the use of the fictitious wave steepness and related surf-similarity parameters in methods that describe the hydraulic and structural response to waves

To assess the hydraulic performance of coastal structures - viz. wave run-up, overtopping and reflection - and to evaluate the stability of the armour layers, use is made of the dimensionless surf similarity parameter, as introduced by Battjes (1974). The front side slope of the structure and the wave steepness are combined in this parameter, also called the Iribarren number. The introduction of the wave steepness was based on the wish to include the effect of the wave period, T, in the surf similarity parameter and hence in the various methods that describe the hydraulic and structural response to waves. The wave steepness to be used in the various methods is the fictitious wave steepness: the ratio of the wave height at the toe of the structure (H) and the fictitious deep-water wavelength (Lo), or rather, the squared value of the local wave period, multiplied by g/2 pi. In deep water the fictitious wave steepness equals the real wave steepness (Ho/Lo), but this is not the case in shallow water, H/Lo is not H/L. The characteristic wave period of a wave field travelling into shallow water is subject to change, due to bathymetry, initial wave breaking, etc. Using the real deep-water wavelength in the expression for the fictitious wave steepness may, therefore, lead to incorrect conclusions when evaluating the key response characteristics in (very) shallow water. To avoid ambiguities and mistakes, it is therefore suggested to refrain from using the wavelength in the expression of the fictitious wave steepness, but to rather only use the local wave period: so = 2 pi Hs/(gT2). A logical next step would be to use "sf" as the notation for the fictitious wave steepness.