### THE EFFECT OF ROUGHNESS ON THE MASS-TRANSPORT OF PROGRESSIVE GRAVITY WAVES

#### Abstract

On the basis of non-viscous small amplitude firstorder theory the maximum value of the horizontal orbital motion at the bed in water of constant depth his given by /U/n yy* »* " r •»** */i where k = /L, H is the wave height crest to trough, T is the period, and L the wave length (L = Sry2jr Arf 2*%/L ). On the basis of finite amplitude wave theory where the particle orbits are not closed ana by the insertion of the viscous laminar boundary layer (the conducti6n solution) the mean drift velocity or mass transport velocity on a perfectly smooth bed is given by Longuet- Higgins (1952) as 7, K H* kcr where <r= /pand K has a maximum value of 0.344 within the boundary layer and a value of 0.313 (i.e. 5/16) just outside the boundary layer. This mass transport current offers a mechanism whereby bed material outside the breaking zone may be transported.

#### Keywords

roughness; mass transport; progressive waves

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