Wave Forecasting in Shallow Water: A New Set of Growth Curves Depending on Bed Roughness

Abstract

Forecasting relationships have been recognized as an important tool to be applied together, or not, with complete numerical modelling in order to reconstruct the wave field in coastal areas properly when the available wave data is limited. In recent years, the literature has offered several comprehensive sets of field experiments investigating the form of the asymptotic, depth-limited wind waves. This has made it possible to reformulate the original deep water equations, taking into account the effects of water depth, if wind waves are locally generated in shallow and confined basins. The present paper is an initial attempt to further contribute to the shallow water forecasting curves which are currently available, also considering the role on the wave generation of a variable equivalent bottom roughness. This can offer the possibility of applying shallow growth curves to a broad variety of contexts, for which bed composition and forms can be different. Simple numerical tests have been conducted to reproduce the fully developed conditions of wave motion with variable roughness values. To validate the new set of equations, they have been applied to a real shallow lake for which both experimental and numerical wave data is available. The comparison of the obtained results is very encouraging in proceeding with this approach.

Keywords

• wind wave growth
• finite depth
• bottom friction
• shallow lake