To reduce the computational costs of numerical studies of gravity wave breaking in the atmosphere, the grid resolution has to be reduced as much as possible. Insufficient resolution of small-scale turbulence demands a proper turbulence parameterization in the framework of a large-eddy simulation (LES). The authors validate three different LES methods-the adaptive local deconvolution method (ALDM), the dynamic Smagorinsky method (DSM), and a naïve central discretization without turbulence parameterization (CDS4)-for three different cases of the breaking of well-defined monochromatic gravity waves. For ALDM, a modification of the numerical flux functions is developed that significantly improves the simulation results in the case of a temporarily very smooth velocity field. The test cases include an unstable and a stable inertia-gravity wave as well as an unstable high-frequency gravity wave. All simulations are carried out both in three-dimensional domains and in two-dimensional domains in which the velocity and vorticity fields are three-dimensional (so-called 2.5D simulations). The results obtained with ALDM and DSM are generally in good agreement with the reference direct numerical simulations as long as the resolution in the direction of the wave vector is sufficiently high. The resolution in the other directions has a weaker influence on the results. The simulations without turbulence parameterization are only successful if the resolution is high and the level of turbulence is comparatively low.@en

We have performed fully resolved three-dimensional numerical simulations of a statically unstable monochromatic inertia-gravity wave using the Boussinesq equations on an f-plane with constant stratification. The chosen parameters represent a gravity wave with almost vertical direction of propagation and a wavelength of 3 km breaking in the middle atmosphere. We initialized the simulation with a statically unstable gravity wave perturbed by its leading transverse normal mode and the leading instability modes of the time-dependent wave breaking in a two-dimensional space. The wave was simulated for approximately 16 h, which is twice the wave period. After the first breaking triggered by the imposed perturbation, two secondary breaking events are observed. Similarities and differences between the three-dimensional and previous two-dimensional solutions of the problem and effects of domain size and initial perturbations are discussed.@en

A systematic approach to the direct numerical simulation (DNS) of breaking upper mesospheric inertia-gravity waves of amplitude close to or above the threshold for static instability is presented. Normal mode or singular vector analysis applied in a frame of reference moving with the phase velocity of the wave (in which the wave is a steady solution) is used to determine the most likely scale and structure of the primary instability and to initialize nonlinear “2.5-D” simulations (with three-dimensional velocity and vorticity fields but depending only on two spatial coordinates). Singular vector analysis is then applied to the time-dependent 2.5-D solution to predict the transition of the breaking event to three-dimensional turbulence and to initialize three-dimensional DNS. The careful choice of the computational domain and the relatively low Reynolds numbers, on the order of 25,000, relevant to breaking waves in the upper mesosphere, makes the three-dimensional DNS tractable with present-day computing clusters. Three test cases are presented: a statically unstable low-frequency inertia-gravity wave, a statically and dynamically stable inertia-gravity wave, and a statically unstable high-frequency gravity wave. The three-dimensional DNS are compared to ensembles of 2.5-D simulations. In general, the decay of the wave and generation of turbulence is faster in three dimensions, but the results are otherwise qualitatively and quantitatively similar, suggesting that results of 2.5-D simulations are meaningful if the domain and initial condition are chosen properly.@en

We present the results of fully resolved direct numerical simulations of monochromatic gravity waves breaking in the middle atmosphere. The simulations are initialized with optimal perurbations of the gives waves. Given a wavelength of 3 km, the required grid sizes range up to 3.6 billion computational cells, depending on the necessary domain size and the turbulence intensity. Our results provide an insight into the mechanics of gravity wave breaking they will be of great value for the validation of lower order methods for the prediction of wave breaking.@en

Geophysical flows including stable stratification and system rotation are a special challenge for turbulence subgrid-sclae models for large-eddy simulation (LES) and hence require validation with suitable test cases. We validate different subgrid-scale models for this kind of flows using a breaking monochromatic inertiagravity wave that has been studied before. We find that the standard Smagorinsky model cannot be recommended while the dynamic Smagorinsky model and the implicit turbulence model ALDM are suitable to simulate this complex flow with high accuracy.@en