Observations of Island Wakes at High Rossby Numbers: Evolution of Submesoscale Vortices and Free Shear Layers

Oceanic vortex evolution on the lee side of Taiwan’s Green Island (~7 km in diameter), where the Kuroshio flows at a speed of 1–1.5 m s−1, is observationally examined and compared to theories and the preceding results of laboratory experiments. In the near wake, recirculation occurs with a relative vorticity of ζ ~ 20f (where f is the planetary vorticity) and subsequently sheds at a combination of periods resulting from the tidal oscillations and the intrinsic time scale of eddy evolution. The tidal oscillations are the predominant processes. Our analysis suggests that an island positioned in the Kuroshio with periodic and cross-stream tidal excursions is analogous to a cross-stream oscillating cylinder. Consequently, the shedding period of the vortex is synchronized to a tidal period occurring close to the intrinsic period. The free shear layer, which is characterized by an ~30f relative vorticity band (2 km wide) and a wavy thermal front, develops between the Kuroshio and recirculation. The frontal wave occurring over a time period of 0.5–2 h resembles Kelvin–Helmholtz instability corresponding to high Re values. For the far wake, repeated cross-wake surveys suggest that cyclonic and anticyclonic vortices are alternatively present at a period close to the period of M2 tides in agreement with near-wake measurements. Repeated along-wake surveys reveal a cyclonic eddy shedding downstream at a speed of 0.35 m s−1, 1/3 of the upstream current speed, from the near wake. In comparing our observations with the results of previous water tank experiments, an Re value of O(103) for the submesoscale wake regime is expected.

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

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 $c_{f}$ is the bottom boundary friction coefficient); in tidal flows, there is an additional dependence on the Keulegan–Carpenter number $KC=U_{0}T/D$ (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 $S=\unicode[STIX]{x1D6FF}^{+}/KC$ where $\unicode[STIX]{x1D6FF}^{+}$ 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 $S\gtrsim 0.1$; (ii) unsteady bubble for $0.06\lesssim S\lesssim 0.1$; and (iii) vortex shedding for $S\lesssim 0.06$. 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 depend on three parameters: (i) the flow aspect ratio $h/D$; (ii) the amplitude of tidal motion relative to the island size, given by $KC$; and (iii) the relative influence of bottom friction to the flow depth, given by $\unicode[STIX]{x1D6FF}^{+}$. A model of wake upwelling based on Ekman pumping from the bottom boundary layer demonstrates that upwelling in the near-wake region of an island scales with $U_{0}(h/D)KC^{1/6}$ and is independent of the wake form. Finally, we demonstrate an intrinsic link between the dynamical eddy scales, predicted by the Ekman pumping model, and the island wake form and stability.