Inception of turbulence at the bed under periodic gravity waves

It is well known that in laboratory studies of wave phenomena in flumes and models the flow is laminar. From field observations, however, it is known that turbulence exists for most or all cases of finite wave motion. An experimental investigation of the range of validity of the theory of mass transport by waves proposed by Longuet-Higgins for a viscous boundary layer at the bottom led to the discovery of the value of the critical Reynolds number at which turbulence occurs on a smooth horizontal bed. This experimental value is compared with theoretical and experimental observations of other authors. The value of the critical Reynolds number was found to be given by Vo δ/v = (π/vT)1/2 H/sinh kd ≈ 160.