Wake Reattachment to a Free-Surface

Wake reattachment to a free-surface. A horizontal cylinder of diameter D is located in shallow water of depth hw, as illustrated in the schematic; D/hw = 0.75. The patterns of averaged streamlines <Ψ>, vorticity <ω>, velocity <V>, and Reynolds stress <u'v'>/U2 are determined independently over the indicated fields of view. The composite images shown in the upper two rows indicate that two cells, rather than a single cell, form in the reattachment region. Foci are identified as F1 and F, a half-saddle point adjacent to the free-surface is designated as S1 , and the location of reattachment to the free-surface is designated by the vertical arrow. In the corresponding pattern of averaged vorticity<ω>, the peak value rapidly decays along the edge of the separation zone; its centerline is indicated by the dashed white line. Regions of positive (thick white line) vorticity are formed in the regions of the foci F1 and F. Patterns of Reynolds stress indicate that relatively high values are maintained along the entire edge of the separation zone and persist with significant values downstream of the reattachment location. These features are related to patterns of instantaneous vorticity and streamline topology (not shown).