Cylinder wakes in shallow oscillatory flow: the coastal island wake problem

摘要

Topographic complexity on continental shelves is the catalyst that transforms the barotropic tide into the secondary and residual circulations that dominate vertical and cross-shelf mixing processes. Island wakes are one such example that are observed to significantly influence the transport and distribution of biological and physical scalars. Despite the importance of island wakes, to date, no sufficient, mechanistic description of the physical processes governing their development exists for the general case of unsteady tidal forcing. Controlled laboratory experiments are necessary for the understanding of this complex flow phenomenon. Here, three-dimensional velocity field measurements of cylinder wakes in shallow-water oscillatory flow are conducted across a parameter space that is typical of tidal flow around shallow islands. The wake form in steady flows is typically described in terms of the stability parameter S = c(f)D/h (where D is the island diameter, h is the water depth and cf is the bottom boundary friction coefficient); in tidal flows, there is an additional dependence on the Keulegan-Carpenter number KC = U0T = D (where U-0 is the tidal velocity amplitude and T is the tidal period). In this study we demonstrate that when the influence of bottom friction is confined to a Stokes boundary layer the stability parameter is given by S = delta(+)/KC where delta(+) is the ratio of the wavelength of the Stokes bottom boundary layer to the depth. Three classes of wake form are observed with decreasing wake stability: (i) steady bubble for S greater than or similar to 0.1; (ii) unsteady bubble for 0.06 less than or similar to S less than or similar to 0.1; and (iii) vortex shedding for S less than or similar to 0.06. Transitions in wake form and wake stability are shown to depend on the magnitude and temporal evolution of the wake return flow. Scaling laws are developed to allow upscaling of the laboratory results to island wakes. Vertical and lateral transport