We present direct numerical simulations of inertia-gravity waves breaking in the middle-upper mesosphere. We consider two different altitudes, which correspond to the Reynolds number of 28 647 and 114 591 based on wavelength and buoyancy period. While the former was studied by Remmler et al., it is here repeated at a higher resolution and serves as a baseline for comparison with the high-Reynolds-number case. The simulations are designed based on the study of Fruman et al., and are initialized by superimposing primary and secondary perturbations to the convectively unstable base wave. Transient growth leads to an almost instantaneous wave breaking and secondary bursts of turbulence. We show that this process is characterized by the formation of fine flow structures that are predominantly located in the vicinity of the wave's least stable point. During the wave breakdown, the energy dissipation rate tends to be an isotropic tensor, whereas it is strongly anisotropic in between the breaking events. We find that the vertical kinetic energy spectra exhibit a clear 5/3 scaling law at instants of intense energy dissipation rate and a cubic power law at calmer periods. The term-by-term energy budget reveals that the pressure term is the most important contributor to the global energy budget, as it couples the vertical and the horizontal kinetic energy. During the breaking events, the local energy transfer is predominantly from the mean to the fluctuating field and the kinetic energy production is in balance with the pseudo kinetic energy dissipation rate.@en

Turbulence in the atmosphere is generally affected by rotation and stratification. The combination of these two effects endows the atmosphere with wavelike motions, which are particularly relevant for the mixing processes in the middle and upper atmosphere. Gravity-waves, for instance, can transfer energy over large distances, carrying energy from where they are created to regions thousands of kilometers away (Fritts and Alexander (2003)). Due to wave instabilities, they break and induce small scale turbulence in the overall large scale flow, thus contributing to the mixing process. In current general circulation models, however, small scale motion is not resolved and instead only parametrized. Hence, understanding the breaking process can potentially lead to improved parametrization models and predictions. Depending on their frequency, gravity-waves can be classified as high-frequency gravity-waves (HGWs) and low-frequency inertia-gravity waves (IGWs). The breaking behavior of IGWs differs fundamentally from HGWs and must be investigated separately (Dunkerton (1997), Achatz and Schmitz (2006), Fruman et al. (2014)). Given that the wave breaking event leads to small scale three-dimensional turbulence, computational investigations must resolve a very large range of dynamic scales of motions (Lelong and Dunkerton (1998) and Fritts et al. (1994)). For HGWs, three-dimensional high resolution Direct Numerical Simulations (DNS) have already been performed, for example, by Fritts et al. (2009) and Remmler et al. (2015). For IGWs, fully threedimensional investigations of a IGW breaking in the upper mesosphere were first presented by Remmler et al. (2012) and Fruman et al. (2014). The present work focuses on turbulence induced by the breaking events of IGWs. We extend the work of Remmler et al. (2012) and Fruman et al. (2014) by performing DNS of an IGW breaking at a lower altitude and correspondingly higher Reynolds number typical of the middle mesosphere. Additionally, we explain the turbulent energy transfer during breaking events and analyze the structure of the turbulence dissipation tensor. Finally, we perform Large-Eddy Simulations (LES) using different models. We compare LES results to our DNS and asses if these models can be used to qualitatively predict breaking events. @en