Gravity wave generation by shear instability of balanced flow

<ul><li> <p>The generation of internal gravity waves from an initially geostrophically balanced flow is&#160;diagnosed in non-hydrostatic numerical simulations of shear instabilities for varied dynamical&#160;regimes. A non-linear decomposition method up to third order in the Rossby number&#160;Ro&#160;is used as the diagnostic tool for a consistent separation of the balanced and unbalanced&#160;motions in the presence of their non-linear coupling. Wave emission is investigated in an&#160;Eady-like and a jet-like flow. For the jet-like case, geostrophic and ageostrophic unstable&#160;modes are used to initialize the flow in different simulations. Gravity wave emission is in&#160;general very weak over a range of values for&#160;Ro. At sufficiently high&#160;Ro, however, when&#160;the condition for symmetric instability is satisfied with negative values of local potential&#160;vorticity, significant wave emission is detected even at the lowest order. This is related to&#160;the occurrence of fast ageostrophic instability modes, generating a wide spectrum of waves.&#160;Thus, gravity waves are excited from the instability of the balanced mode to lowest order&#160;only if the condition of symmetric instability is satisfied and ageostrophic unstable modes&#160;obtain finite growth rates.</p> </li> </ul>