Island wakes in deep and shallow water

Island wakes in deep and shallow water

Sketch of the flow field around a cylinder (circular island), showing the frictional boundary layer and the forces experienced by a water particle as it moves along a streamline.

a) no separation, laminar boundary layer b) vortex pair with central return flow c) wake formation with wave disturbances along the current/wake interface d) von Karman vortex street Flow around an obstacle under different Reynolds numbers.

Reynolds numbers observed in towing tanks for different types of flow around islands. flat plate other shapes type of flow Re < 1 Re < 0. 5 laminar flow, no separation Re>= 1 Re > 2 - 30 vortex pair with central return flow Re >= 10 Re > 40 - 70 wake formation with wave disturbances Re >> 10 Re > 60 - 90 von Karman vortex street

Island wakes in deep water and in the atmosphere Fig. 3

Reconstruction of Johnston Atoll's wake from longline drifts The right figure shows the orientation and the background current, which was about 0. 5 m s-1 towards north west (numbers are in m s-1). The left figure shows the reconstructed eddy field in a coordinate system relative to the mean flow (which goes to the left, but the figure is drawn as if Johnston Atoll were dragged through the water towards the right, pulling the wake behind it). Red arrows indicate observed longline drifts (the central part is the set longline, the arrows on either side indicate the movement of the two ends of the longline). Blue arrows indicate the drift of the ship. Black lines give the inferred streamlines. Pink eddies rotate clockwise, green eddies anti-clockwise. The entire vortex street moved towards 320° at 0. 45 m s-1. After Barkley (1972).

Comparison of vortex street parameters in the ocean and in the atmosphere. From Barkley (1972) parameter Ocean (Johnston Atoll) Atmosphere (Madeira) effective island diameter 26 km 40 km wavelength or pitch of vortex street 160 km 190 km width between vortex rows 55 km 83 km speed of incident flow 0. 6 m s-1 10 m s-1 translation speed of wake 0. 45 m s-1 period of eddy pair formation 4 days 7. 2 hours Reynolds number 70 90 eddy viscosity coefficient 220 m 2 s-1 7. 5 m s-1 4, 400 m 2 s-1

Island wakes in shallow water

Surface temperature and currents behind Rattray island, Great Barrier Reef. The background current is southeastward, somewhat oblique to the island. As a result, the northern vortex is clearly stronger than the southern one, but the weak northward current to the south east of the island indicates that a second vortex is present. Isotherms are contoured every 0. 1°C, with the lowest temperature indicated as less than 25. 6°C. The lower temperatures in the island's wake are the result of increased mixing, which brings colder water to the surface. The broken line shows the ship's track along which the measurements were made.

Areal photographs of Rattray island, Great Barrier Reef of Australia, and its wake. The tidal current approaches the island from the top right in the first image and from the top left in the second image. It meets the island at a somewhat oblique angle, which results in one vortex being stronger than the other. The photographs show only the main vortex. The size of the island can be estimated by the wake of the speed boat seen in the first image.

Shallow water wakes

Shallow water wake model Ekman benthic boundary layer model

Wolanski island parameter

3 D Numerical model results

Currents around Poppy Point on Whitsunday Island, Great Barrier Reef. Currents were measured at points A and B and visually estimated elsewhere. Stippling denotes quiet water. Note the extremely small scale. Adapted from Alldredge and Hamner (1980).

Aggregation of zooplankton in the lee eddy of Poppy Point produced by the tidal current. The top diagram compares zooplankton biomass in the eddy with the background level found in Hunt Channel. The bottom diagram shows currents at locations A and B of Figure 7. 7. The figure shows one half of a tidal cycle; as can be seen, slack tide occurred just before 8 a. m. (8. 00 h) and after 1 p. m. (13. 00 h). Adapted from Alldredge and Hamner (1980).

Lake Eyre, South Australia, shortly after flooding in January 1984. Lake Eyre is maintained by a large inland drainage system but is mostly a dry salt lake. The flow pattern after flooding is made visible by the contrast between water stemming from the dissolved salt crust and water containing fine silt. The figures show a variety of flow phenomena in 1. 5 m water depth, including vortex formation behind a small sand island.

Re = (inertial force / friction force) = (inertial force / Coriolis force) (Coriolis force / friction force) = Ro / E

The transition between the various types of flow past islands in a diagram of Rossby number vs. Ekman number. Adapted from Pattiarachi et al. (1987).

a) Topography of Koombana Bay, about 150 km south of Perth. Depth contours are in metres. b) Tidal current 6 hours after high water in Leschenault Inlet, derived from a numerical model. The associated bipole is indicated by the red and yellow ellipses. c) Water movement derived from drogue tracks. Dipoles off the West Australian coast.

Fluid flow behind a cylinder as seen in a laboratory tank. First diagram: A von Karman vortex street produced by a cylindrical obstacle. Second diagram: A second cylinder is added to the experiment. Its radius R is one tenth of the radius of the main cylinder, and it is positioned a distance R behind the main cylinder and offset from the axis of the flow by the same distance R. Eddy shedding is completely suppressed. In both diagrams the cylinder is on the left; the diagrams start at a distance 16 R behind the cylinder and finish at about 100 R.