Waves

Abstract

We now come to the study of similarity as applied to waves, certainly the most difficult subject encountered so far. When the application of the exact method of the theory of similarity becomes impossible, then, as has repeatedly been shown in the preceding chapters, a model is designed using mathematical expressions describing the relationships between the quantities involved. Unfortunately, an adequate mathematical theory exists only for wave motion of an ideal (inviscid) fluid. This theory, as is clear from its definition, cannot provide information on such quantities as shear stress, roughness, viscosity, boundary layer thickness and so on, which are of importance in the design of a model. Reliable information on the oscillatory boundary layer is available solely for viscous (laminar) fluid motion over a smooth plain bed. Considering that in almost all cases of civil engineering practice fluid motion is turbulent, while the bed is neither smooth nor plain, it will be clear how limited is the application of existing reliable methods when practical problems occur. It is small wonder then that, to date, no firm method has been established for the design of a small scale wave and/or tidal model where the influence of roughness, viscosity, shear stress, etc. is important (as in all models with mobile bed). Very often the design depends simply on experience and intuition rather than on any method at all.