The “slip law” of the free surface |
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| Authors: | G T Csanady |
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| Institution: | (1) Old Dominion University, 23529-0276 Norfolk, VA, USA |
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| Abstract: | A “slip law” connects the excess velocity or “slip” of a wind-blown water surface, relative to the motion in the middle of
the mixed layer, to the wind stress, the wind-wave field, and buoyancy flux. An inner layer-outer layer model of the turbulent
shear flow in the mixed layer is appropriate, as for a turbulent boundary layer or Ekman layer over a solid surface, allowing,
however, for turbulent kinetic energy transfer from the air-side via breaking waves, and for Stokes drift. Asymptotic matching
of the velocity distributions in inner and outer portions of the mixed layer yields a slip law of logarithmic form, akin to
the drag law of a turbulent boundary layer. The dominant independent variable is the ratio of water-side roughness length
to mixed layer depth or turbulent Ekman depth. Convection due to surface cooling is also an important influence, reducing
surface slip. Water-side roughness length is a wind-wave property, varying with wind speed similarly to air-side roughness.
Slip velocity is typically 20 times water-side friction velocity or 3% of wind speed, varying within a range of about 2 to
4.5%. A linearized model of turbulent kinetic energy distribution shows much higher values near the surface than in a wall
layer. Nondimensional dissipation peaks at a value of about eight, a short distance below the surface. |
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| Keywords: | Sea surface velocity oceanic turbulence mixed layer wind-waves and turbulence air-sea interaction |
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