EWM 26: On wave-induced viscosity: Revealing a long-standing mystery by Dirk Olbers

On wave-induced viscosity: Revealing a long-standing mystery by Dirk Olbers (Alfred-Wegener-Institut) We revisit Mueller’s (1976) analysis on wave-induced viscosities. The interaction of small scale internal gravity waves with a large-scale shear flow was analyzed and a very large vertical viscosity, of order 1m2s−1, was found. It could never be substantiated in observed relations between wave-induced stress and mean vertical shear. The origin of the failure of the theory, however, was never revealed. On the contrary, Mueller’s approach is still used for the inter action of waves with a mean horizontal shear and leading to reasonably sized wave-induced horizontal viscosities. Mueller’s theory is based on seemingly harmless assumptions– an ocean wave climate was taken as basis, an isotropic Garrett-Munk state. We solve the energy balance (radiation balance) of the problem exactly, with forcing and boundary conditions at top and bottom, and show where the failure occurs. The interactions lead to an intrinsically anisotropic state which is non-viscous. Only in case that vertical propagation times are less than charac teristic interaction times of the wave-mean flow process viscous behavior becomes possible and much smaller viscosities apply which are orders of magnitude smaller than Mueller’s values.