Description: A new, energetically, and dynamically consistent closure for the lee wave drag on the large-scale circulation is developed and tested in idealized and realistic ocean model simulations. The closure is based on the radiative transfer equation for internal gravity waves, integrated over wavenumber space, and consists of two lee wave energy compartments for up- and downward propagating waves, which can be cointegrated in an ocean model. Mean parameters for vertical propagation, mean–flow interaction, and the vertical wave momentum flux are calculated assuming that the lee waves stay close to the spectral shape given by linear theory of their generation. Idealized model simulations demonstrate how lee waves are generated and interact with the mean flow and contribute to mixing, and document parameter sensitivities. A realistic eddy-permitting global model at 1/10° resolution coupled to the new closure yields a globally integrated energy flux of 0.27 TW into the lee wave field. The bottom lee wave stress on the mean flow can be locally as large as the surface wind stress and can reach into the surface layer. The interior energy transfers by the stress are directed from the mean flow to the waves, but this often reverses, for example, in the Southern Ocean in case of shear reversal close to the bottom. The global integral of the interior energy transfers from mean flow to waves is 0.14 TW, while 0.04 TW is driving the mean flow, but this share depends on parameter choices for nonlinear effects.

Description: The generation of internal gravity waves from an initially geostrophically balanced flow is diagnosed in nonhydrostatic numerical simulations of shear instabilities for varied dynamical regimes. A nonlinear decomposition method up to third order in the Rossby number (Ro) is used as the diagnostic tool for a consistent separation of the balanced and unbalanced motions in the presence of their nonlinear coupling. Wave emission is investigated in an Eady-like and a jet-like flow. For the jet-like case, geostrophic and ageostrophic unstable modes are used to initialize the flow in different simulations. Gravity wave emission is in general very weak over a range of values for Ro. At sufficiently high Ro, however, when the condition for symmetric instability is satisfied with negative values of local potential vorticity, significant wave emission is detected even at the lowest order. This is related to the occurrence of fast ageostrophic instability modes, generating a wide spectrum of waves. Thus, gravity waves are excited from the instability of the balanced mode to lowest order only if the condition of symmetric instability is satisfied and ageostrophic unstable modes obtain finite growth rates.