1 Multi-scale methods for geophysical flows by Christian L.E. Franzke et al -- 2 The interior energy pathway: inertial gravity wave emission by oceanic flows by Jin-Song von Storch et al -- 3 The IDEMIX model: parameterization of internal gravity waves for circulation models of ocean and atmosphere by Dirk Olbers et al -- 4 Observations and models of low mode internal waves in the ocean by Christian Mertens et al -- 5 Toward consistent subgrid momentum closures in ocean models by Sergey Danilov et al -- 6 Diagnosing and parameterizing the effects of oceanic eddies by Alexa Griesel et al -- 7 Entropy production in turbulence parameterizations by Almut Gassmann et al -- 8 Reducing spurious diapycnal mixing in ocean models by Knut Klingbeil et al -- 9 Diffuse interface approaches in atmosphere and ocean - modeling and numerical implementation by Harald Garcke et al -- Index.

This book describes a recent effort combining interdisciplinary expertise within the Collaborative Research Centre “Energy transfers in atmosphere and ocean” (TRR-181), which was funded by the German Research Foundation (DFG). Energy transfers between the three dynamical regimes – small-scale turbulence, internal gravity waves and geostrophically balanced motion – are fundamental to the energy cycle of both the atmosphere and the ocean. Nonetheless, they remain poorly understood and quantified, and have yet to be adequately represented in today’s climate models. Since interactions between the dynamical regimes ultimately link the smallest scales to the largest ones through a range of complex processes, understanding these interactions is essential to constructing atmosphere and ocean models and to predicting the future climate. To this end, TRR 181 combines expertise in applied mathematics, meteorology, and physical oceanography. This book provides an overview of representative specific topics addressed by TRR 181, ranging from - a review of a coherent hierarchy of models using consistent scaling and approximations, and revealing the underlying Hamiltonian structure - a systematic derivation and implementation of stochastic and backscatter parameterisations - an exploration of the dissipation of large-scale mean or eddying balanced flow and ocean eddy parameterisations; and - a study on gravity wave breaking and mixing, the interaction of waves with the mean flow and stratification, wave-wave interactions and gravity wave parameterisations to topics of a more numerical nature such as the spurious mixing and dissipation of advection schemes, and direct numerical simulations of surface waves at the air-sea interface. In TRR 181, the process-oriented topics presented here are complemented by an operationally oriented synthesis focusing on two climate models currently being developed in Germany. In this way, the goal of TRR 181 is to help reduce the biases in and increase the accuracy of atmosphere and ocean models, and ultimately to improve climate models and climate predictions.