Model of Vertical Mixing Induced by Wind Waves

—Formulas for the vertical wind-wave-induced mixing coefficient are obtained. For this purpose, in the Navier–Stokes equations the flow velocity is decomposed into four components, namely, mean flow, wave orbital motion, wave-induced turbulent flow fluctuations, and background turbulent fluctuations. Such a decomposition makes it possible to distinguish the wave stress Re w in the Reynolds equations as an addition to the background stress Re b . For the background turbulent fluctuations the Prandtl approximation is used for closure of Re w . This leads to an implicit expression for the wave-induced vertical mixing function . The finite expression for is determined using author’s results for the turbulent viscosity in the wave zone found earlier within the framework of the three-layer conception for the air-water interface. The explicit expression for the function is linear with respect to the wave amplitude a ( z ) at the depth z and the friction velocity u * in air. Since the wave amplitude decreases exponentially as a function of the depth, this result for means the possibility of strengthening the wave impact on vertical mixing as compared with the well-known cubic dependence of .