Karman vortex streets in wakes of islands.

Abstract

W satellites equipped with narrow-angle cameras have revealed the existence of mesoscale eddies, which are on a scale too small to be delineated by the standard weather observation network and are too large to be seen by an observer on the ground or even pictured from a high-flying aircraft. Hubert and Krueger have described the characteristic properties of mesoscale eddies formed in the wakes of islands that are steep-sided and extend far above the lowlying inversion. These eddies are made visible by patterns in stratocumulus clouds lying beneath a strong inversion about 0.5 to 2.0 km above the ocean surface and have been observed to persist several hundred kilometers downstream. The bandwidth of the eddies is of the order of the cross-stream diameter of the island. Under favorable conditions, the pattern of the eddies bears a strong resemblance to the classical Karman vortex street pattern observed in laboratory studies of wakes behind obstacles. Figure 1 is a typical example of these eddies in the vicinity of the Madeira Islands. Recently, Chopra and Hubert examined the properties of the eddies downstream of the Tenerife and the Gran Canaria Islands in the light of this apparent resemblance between the meteorological mesoscale eddies and the classical vortex street pattern of Fig. 2. This analogy is analyzed further in this note. Viscosity plays two roles in the flow pattern of a Karman vortex street. First, it leads to the formation of the boundary layer in which vorticity is generated and the vortex pairs are formed, the vortices being shed alternately near each edge of the obstacle. Second, the strength of the eddies is dissipated by the mechanism of diffusion; the size of an eddy increases, and its strength decreases as it propagates downstream, until its region of influence overlaps that of a neighboring eddy of opposite circulation. In all of the other respects, the fluid may be regarded as perfect (inviscid). The rate N of shedding of the eddy pair is given by .V ue/a = (l/a)foo (k/2a) taDh(irh/a)] (1) where ue is the speed of propagation downstream of the eddies in a coordinate system fixed to the obstacle, UQ is the speed of the undisturbed flow, a is the longitudinal spacing (pitch) between two eddies of similar circulation of strength k, and h is the lateral spacing (bandwidth) between the two vortex rows. Drag and Spacing Ratio