Forcing of oceanic mean flows by dissipating internal tides

We present a theoretical study of the effective mean force exerted on an oceanic mean flow due to the presence of small-amplitude internal waves that are forced by a barotropic tide flowing over a topography and are also subject to dissipation. Although the details of our computation are quite different, we recover the main action-at-a-distance result familiar from atmospheric wave-mean interaction theory, namely that the effective mean force that is felt by the mean flow is located in regions of wave dissipation, and not necessarily near the topographic wave source. Specifically, using a perturbation series in small wave amplitude, we compute the three-dimensional leading-order wave field using a Green's function approach, derive an explicit expression for the leading-order effective mean force at the next order within the framework of generalized Lagrangian-mean theory, discuss in detail the range of situations in which a strong, secularly growing mean-flow response can be expected, and finally compute the effective mean force numerically in a number of illustrative examples with simple topographies.