Note on seabed shear stress beneath bichromatic and bidirectional waves for large bed roughness

Abstract

The seabed shear stress beneath bichromatic and bidirectional waves is presented. The approach is analytical using the constant time-invariant eddy viscosity representation of Christoffersen and Jonsson (1985) for rough turbulent boundary layers under monochromatic waves for large seabed roughness. This formulation is extended to calculate the maximum bed shear stress beneath bichromatic and bidirectional waves by vectorial superposition of the shear stresses for each harmonic wave. Examples of results are given for bichromatic and unidirectional waves as well as bichromatic and bidirectional waves. Comparisons are also made with an equivalent monochromatic wave. The results appear to be in qualitative agreement with physical expectations. Finally, comparison is made with data from small scale laboratory experiments for seabed shear stress beneath bichromatic and unidirectional waves for large bed roughness yielding fair agreement between predictions and data.