The differentially heated rotating annulus is a widely studied tabletop-size laboratory model of the general mid-latitude atmospheric circulation. The two most relevant factors of cyclogenesis, namely rotation and meridional temperature gradient are quite well captured in this simple arrangement. The radial temperature difference in the cylindrical tank and its rotation rate can be set so that the isothermal surfaces in the bulk tilt, leading to the formation of baroclinic waves. The signatures of these waves at the free water surface have been analyzed via infrared thermography in a wide range of rotation rates (keeping the radial temperature difference constant) and under different initial conditions. In parallel to the laboratory experiments, five groups of the MetStröm collaboration have conducted numerical simulations in the same parameter regime using different approaches and solvers, and applying different initial conditions and perturbations. The experimentally and numerically obtained baroclinic wave patterns have been evaluated and compared in terms of their dominant wave modes, spatio-temporal variance properties and drift rates. Thus certain "benchmarks" have been created that can later be used as test cases for atmospheric numerical model validation.@en

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

Durran's pseudo-incompressible equations are integrated in a mass and momentum conserving way with a new implicit turbulence model. This system is soundproof, which has two major advantages over fully compressible systems: the Courant-Friedrichs-Lewy (CFL) condition for stable time advancement is no longer dictated by the speed of sound and all waves in the model are clearly gravity waves (GW). Thus, the pseudo-incompressible equations are an ideal laboratory model for studying GW generation, propagation, and breaking. Gravity wave breaking creates turbulence that needs to be parameterized. For the first time the adaptive local deconvolution method (ALDM) for implicit large-eddy simulation (ILES) is applied to non- Boussinesq stratified flows. ALDM provides a turbulence model that is fully merged with the discretization of the flux function. In the context of non-Boussinesq stratified flows this poses some new numerical challenges-the solution of which is presented in this text. In numerical test cases the authors show the agreement of the results with the literature (Robert's hot-cold bubble test case), they present the sensitivity to the model's resolution and discretization, and they demonstrate qualitatively the behavior of the implicit turbulence model for a 2D breaking gravity wave packet.@en

The differentially heated rotating annulus is a classical experiment for the investigation of baroclinic flows and can be regarded as a strongly simplified laboratory model of the atmosphere in mid-latitudes. Data of this experiment, measured at the BTU Cottbus-Senftenberg, are used to validate two numerical finite-volume models (INCA and cylFloit) which differ basically in their grid structure. Both models employ an implicit parameterization of the subgrid-scale turbulence by the Adaptive Local Deconvolution Method (ALDM). One part of the laboratory procedure, which is commonly neglected in simulations, is the annulus spin-up. During this phase the annulus is accelerated from a state of rest to a desired angular velocity. We use a simple modelling approach of the spin-up to investigate whether it increases the agreement between experiment and simulation. The model validation compares the azimuthal mode numbers of the baroclinic waves and does a principal component analysis of time series of the temperature field. The Eady model of baroclinic instability provides a guideline for the qualitative understanding of the observations.@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