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An Observational Study of Vortex Spacing in Island Wake Vortex Streets

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  • 1 The Pennsylvania State University, University Park, Pennsylvania
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Abstract

Vortex streets are a frequent occurrence in stratocumulus-topped flow downwind of mountainous islands. Theoretical studies dating back to von Kármán, supported by laboratory and numerical studies, have yielded similarity theories for the size and spacing of these vortices behind bluff bodies. Despite dynamical differences between such two-dimensional flows and the three-dimensional flow past isolated islands, satellite case studies suggest these geometric similarities may also hold for the atmospheric case. In this study, two of the resulting dimensionless ratios are measured using satellite imagery. One is the aspect ratio between cross-street and along-street spacing of the vortices. The second is the ratio of the cross-street spacing to the crosswind width of the island. A 30-image sample from the Aqua and Terra Moderate Resolution Imaging Spectroradiometer satellites is analyzed to obtain these ratios. The resulting set of values for the two dimensionless ratios is tested against the values found in bluff body studies. The aspect ratio is tested against the value of 0.28 resulting from von Kármán’s inviscid theory, and the dimensionless width ratio is tested against the value of 1.2 from Tyler’s laboratory study of flow around a bluff body. It is found that atmospheric vortex streets do indeed follow the geometric similarity theories, but with different values for the two ratios than those predicted by von Kármán and Tyler. The aspect ratio is larger than predicted as is the dimensionless width ratio. Both differences are consistent with the turbulent diffusion of vorticity in the wake of the island. The vortex streets more closely follow inviscid theory close to the island, with vortex expansion taking place a few vortex diameters downwind of the island.

Corresponding author address: Dr. George S. Young, 503 Walker Building, Meteorology Department, The Pennsylvania State University, University Park, PA 16802. Email: young@meteo.psu.edu

Abstract

Vortex streets are a frequent occurrence in stratocumulus-topped flow downwind of mountainous islands. Theoretical studies dating back to von Kármán, supported by laboratory and numerical studies, have yielded similarity theories for the size and spacing of these vortices behind bluff bodies. Despite dynamical differences between such two-dimensional flows and the three-dimensional flow past isolated islands, satellite case studies suggest these geometric similarities may also hold for the atmospheric case. In this study, two of the resulting dimensionless ratios are measured using satellite imagery. One is the aspect ratio between cross-street and along-street spacing of the vortices. The second is the ratio of the cross-street spacing to the crosswind width of the island. A 30-image sample from the Aqua and Terra Moderate Resolution Imaging Spectroradiometer satellites is analyzed to obtain these ratios. The resulting set of values for the two dimensionless ratios is tested against the values found in bluff body studies. The aspect ratio is tested against the value of 0.28 resulting from von Kármán’s inviscid theory, and the dimensionless width ratio is tested against the value of 1.2 from Tyler’s laboratory study of flow around a bluff body. It is found that atmospheric vortex streets do indeed follow the geometric similarity theories, but with different values for the two ratios than those predicted by von Kármán and Tyler. The aspect ratio is larger than predicted as is the dimensionless width ratio. Both differences are consistent with the turbulent diffusion of vorticity in the wake of the island. The vortex streets more closely follow inviscid theory close to the island, with vortex expansion taking place a few vortex diameters downwind of the island.

Corresponding author address: Dr. George S. Young, 503 Walker Building, Meteorology Department, The Pennsylvania State University, University Park, PA 16802. Email: young@meteo.psu.edu

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