The effects of variation in wave period and flow asymmetry in sediment dynamics
The results of laboratory experiments are described, relating to aspects of hydrodynamics and sediment dynamics under second-order Stokes type waves (or flows), of varying degrees of asymmetry. The majority of the measurements related to laminar and/or transitional flow conditions and were made using an oscillating trolley apparatus. The transition to turbulence over smooth beds has been reported previously in terms of a (single) critical flow amplitude Reynolds number, Recrit=U∞a/ν. On the basis of observations undertaken using sinusoidal flows (Li, 1954) and during the present study, this is found to be the case for wave periods of T>3.5s, where mean Recrit=1.66×105. However, for T<3.5s, it is shown that Recrit decreases in proportion to T. On the basis of the observations made by Li (1954), Manohar (1955) and during the present study, transition over rough (granular) beds is described by Recrit=c(a/D), where c is a coefficient that, for relatively fine sediment (D<275μm), is a linear function of T; for relatively coarse sediment (D>421μm), it is a linear function of D. At large values of Recrit, corresponding to longer wave periods together with relatively small bed roughness length-scales, the observed values deviate from the rough-bed relationship and tend towards the smooth-bed limiting value. Flow asymmetry acts to stabilise the boundary layer, increasing either the critical boundary Reynolds number RE 2ν /ω ν crit c =U (in the case of smooth beds), or Recrit (in the case of rough beds), following a non-linear relationship. Regulating mechanisms are proposed by which the transition to turbulence is governed over (relatively) smooth and/or rough beds. Of principle importance is the balance between the stabilising effect of fluid acceleration and the destabilising effects of vertical gradients in the horizontal velocity (thought to be important in regulating transition over a smooth-bed) and localised eddy formation around individual grains on the bed (similarly over rough beds). The threshold of motion for non-cohesive, sand-sized sediment is expressed typically as a critical bed shear stress amplitude, τo, relative to the resistant properties of individual grains (due to gravity). On this basis, numerous critical shear stress (e.g. the well known approach of Shields, 1936) and velocity amplitude relationships have been presented elsewhere. Previously, Voulgaris et al. (1995) have identified that a higher τo is required to cause threshold at smaller wave periods. On the basis of a large number of observations undertaken (elsewhere, and as part of the present study) using similar equipment, a negative linear relationship has been established between T and τo; this becomes progressively more significant, for threshold occurring under larger values of Re (into the transitional regime). Flow asymmetry has the effect of increasing τo crit; however, the critical orbital diameter for given conditions remains approximately constant, irrespective of the asymmetry. Using these data, in combination with detailed observations of the phase of the onset and the subsequent duration of sediment motion, it is suggested that (especially under (near) laminar flows) the threshold of motion is in response to a ‘time-‘ or ‘phase-mean’ shear stress, corresponding to some form of cumulative force. In addition, under turbulent or partially turbulent flow conditions, the stochastic distribution of the instantaneous shear stress is broader under waves of larger T and/or smaller R; this permits similarity in the occurrence of high-shear events, over a range of conditions. However, the mean τ0 crit decreases. Hence, an artefact or anomalous decrease is included, at longer wave periods, in the (time-mean) peak value of τo crit used to represent such flows.