Nonlinear Formulation of the Bulk Surface Stress over Breaking Waves: Feedback Mechanisms from Air-flow Separation |
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Authors: | James A Mueller Fabrice Veron |
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Institution: | (1) College of Marine and Earth Studies, University of Delaware, 112C Robinson Hall, Newark, DE 19716, USA |
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Abstract: | Historically, our understanding of the air-sea surface stress has been derived from engineering studies of turbulent flows
over flat solid surfaces, and more recently, over rigid complex geometries. Over the ocean however, the presence of a free,
deformable, moving surface gives rise to a more complicated drag formulation. In fact, within the constant-stress turbulent
atmospheric boundary layer over the ocean, the total air-sea stress not only includes the traditional turbulent and viscous
components but also incorporates surface-wave effects such as wave growth or decay, air-flow separation, and surface separation
in the form of sea-spray droplets. Because each individual stress component depends on and alters the sea state, a simple
linear addition of all stress components is too simplistic. In this paper we present a model of the air-sea surface stress
that incorporates air-flow separation and its effects on the other stress components, such as a reduction of the surface viscous
stress in the separated region as suggested by recent measurements. Naturally, the inclusion of these effects leads to a non-linear
stress formulation. This model, which uses a variable normalized dissipation rate of breaking waves and normalized length
of the separation bubble, reproduces the observed features of the drag coefficient from low to high wind speeds despite extrapolating
empirical wave spectra and breaking wave statistics beyond known limits. The model shows the saturation of the drag coefficient
at high wind speeds for both field and laboratory fetches, suggesting that air-flow separation over ocean waves and its accompanying
effects may play a significant role in the physics of the air-sea stress, at least at high wind speeds. |
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Keywords: | Air-flow separation Breaking wind waves Sea drag Sea roughness Wave boundary layer |
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