On Transverse Secondary Flows in Wave Channels

Abstract

The viscous boundary layer analysis for the sidewalls of a wave tank is presented for the case of two-dimensional waves of small amplitude traveling along the channel length. The second-order transverse streaming motion induced in the interior of the channel by the sidewall layers is determined. The calculations extend the work of Mei and Liu [1] which examined the effect of sidewalls on the longitudinal streaming motion. The intensity of the transverse streaming flow is found to increase as the depth to wavelength ratio decreases, and is found to be significant for typical wave tanks that generally have a depth to width ratio between one-half and one-fourth. The present results are useful if accurate conclusions concerning mass transport in the open ocean are to be made from laboratory studies. Furthermore, the results may offer an explanation for some of the laboratory observations already in the literature.