T5: Gravity Wave Genesis, Break-up and Dissipation

Gravity waves are oscillatory motions in the stably stratified atmosphere and ocean where the buoyancy force acts as restoring force. Localized packets of gravity waves can travel long distances, transferring thereby momentum between remote regions of the atmosphere and ocean. For instance, they are generated by orography, convection, fronts and boundary layers and transfer momentum to the middle atmosphere and to the deep ocean, where they break into turbulence and interact with the large-scale circulations. How do they break and what is their interaction with the mean flow? How does this depend on the wave generation and the environmental conditions? How can we best represent them in climate models? These are the questions that this project wants to address.

The project is organized in 3 work packages, each addressing different but related aspects of gravity waves: (i) linear stability, (ii) nonlinear instability and breakdown, and (iii) turbulent state. The goal is to provide new conditions of wave break-up and new estimates of dissipation rates vs secondary emission as needed for the gravity-wave parametrizations considered in TRR 181, namely, MS-GWaM, IDEMIX-A in the atmosphere and IDEMIX in the ocean. In this way, we are strongly linked with projects W1 and W4 on gravity-wave parametrization, and with S2 and L5 on parametrizations in climate models.

• The turbulence analysis will use direct numerical simulation to faithfully represent the spatio-temporal intermittency between the turbulence regions and the wave background. We will characterize dissipation properties (mean, intermittency, scales), the direction and spectrum of secondary emission, and the resolution requirements (Reynolds number sensitivity).
• The nonlinear stability analysis will equally benefit from the accuracy of direct numerical simulation to provide dynamic, nonlinear criteria for instability and wave break-up beyond the classical Richardson criterion. We will use the adjoint method to determine the critical perturbation energy threshold necessary for wave break-up, and we will determine the optimal (minimal) perturbation to trigger break-up in different background states.
• The linear stability analysis will refine the determination of the stability-instability boundary in the parameter space. We will use analytical and dynamical systems based on numerical methods for large-scale studies to determine the dependence of the model growth rates in different function spaces of configuration parameters.
• The nonlinear and linear analysis will provide the cases for the turbulence analysis. In turn, the nonlinear and linear analysis will study the stability properties of the secondary waves observed in the turbulence analysis. Results from the three work packages will be used to provide new conditions for wave break-up and estimates of dissipation, in particular, as needed in the prognostic equations for MS-GWaM and IDEMIX(-A) in project W1.