## Inertia gravity waves breaking in the middle atmosphere: energy transfer and dissipation tensor anisotropy

Pestana, T., Thalhammer, M., Hickel, S. (2020) *Journal of the Atmospheric Sciences *77: 3193-3210. doi: 10.1175/JAS-D-19-0342.1

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.

## Validation of large-eddy simulation methods for gravity wave breaking

Remmler, S., Hickel, S., Fruman, M.D., Achatz, U. (2015) *Journal of the Atmospheric Sciences* 72: 3537-3562. doi: 10.1175/JAS-D-14-0321.1

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). We consider 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.

## Benchmarking in a rotating annulus: A comparative experimental and numerical study of baroclinic wave dynamics

Vincze, M., Borchert, S., Achatz, U., Von Larcher, T., Baumann, M., Liersch, C., Remmler, S., Beck, T., Alexandrov, K.D., Egbers, C., Fröhlich, J., Heuveline, V., Hickel, S., Harlander, U. (2015) *Meteorologische Zeitschrift* 23: 611-635. doi: 10.1127/metz/2014/0600

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.

## Finite-volume models with implicit subgrid-scale parameterization for the differentially heated rotating annulus

Borchert, S., Achatz, U., Remmler, S., Hickel, S., Harlander, U., Vincze, M., Alexandrov, K.D., Rieper, F., Heppelmann, T., Dolaptchiev, S.I. (2014) *Meteorologische Zeitschrift* 23: 561-580. doi: 10.1127/metz/2014/0548

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.

## On the construction of a direct numerical simulation of a breaking inertia-gravity wave in the upper-mesosphere

Fruman, M.D., Remmler, S., Achatz, U., Hickel, S. (2014) *Journal of Geophysical Research *119: 11613-11640. doi: 10.1002/2014JD022046

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

## Spectral eddy viscosity of stratified turbulence

Remmler, S., Hickel, S. (2014)*Journal of Fluid Mechanics* 755, R6. doi: 10.1017/jfm.2014.423

The spectral eddy viscosity (SEV) concept is a handy tool for the derivation of large-eddy simulation (LES) turbulence models and for the evaluation of their performance in predicting the spectral energy transfer. We compute this quantity by filtering and truncating fully resolved turbulence data from direct numerical simulations (DNS) of neutrally and stably stratified homogeneous turbulence. The results qualitatively confirm the plateau–cusp shape, which is often assumed to be universal, but show a strong dependence on the test filter size. Increasing stable stratification not only breaks the isotropy of the SEV but also modifies its basic shape, which poses a great challenge for implicit and explicit LES methods. We find indications that for stably stratified turbulence it is necessary to use different subgrid-scale (SGS) models for the horizontal and vertical velocity components. Our data disprove models that assume a constant positive effective turbulent Prandtl number.

## On the application of WKB theory for the simulation of the weakly nonlinear dynamics of gravity waves

Muraschko, J., Fruman, M.D., Achatz, U., Hickel, S., Toledo, Y. (2015) *Quarterly Journal of the Royal Meteorological Society* 141: 676-697. doi: 10.1002/qj.2381

The dynamics of internal gravity waves is modelled using Wentzel–Kramer–Brillouin (WKB) theory in position–wave number phase space. A transport equation for the phase-space wave-action density is derived for describing one-dimensional wave fields in a background with height-dependent stratification and height- and time-dependent horizontal-mean horizontal wind, where the mean wind is coupled to the waves through the divergence of the mean vertical flux of horizontal momentum associated with the waves.

## Direct numerical simulation of a breaking inertia-gravity wave

Remmler, S., Fruman, M.D., Hickel, S. (2013) *Journal of Fluid Mechanics *722: 424-436. doi: 10.1017/jfm.2013.108

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.

## A conservative integration of the pseudo-incompressible equations with implicit turbulence parameterization

Rieper, F., Hickel, S., Achatz, U. (2013)*Monthly Weather Review* 141: 861-886. doi: 10.1175/MWR-D-12-00026.1

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).

## Direct and large-eddy simulation of stratified turbulence

Remmler, S., Hickel, S. (2012) *International Journal of Heat and Fluid Flow* 35: 13-24. doi: 10.1016/j.ijheatfluidflow.2012.03.009

Simulations of geophysical turbulent flows require a robust and accurate subgrid-scale turbulence modeling. To evaluate turbulence models for stably stratified flows, we performed direct numerical simulations (DNSs) of the transition of the three-dimensional Taylor–Green vortex and of homogeneous stratified turbulence with large-scale horizontal forcing.

## Spectral structure of stratified turbulence: Direct Numerical Simulations and predictions by Large Eddy Simulation

Remmler, S., Hickel, S. (2013) *Theoretical and Computational Fluid Dynamics *27: 319-336. doi: 10.1007/s00162-012-0259-9

Density stratification has a strong impact on turbulence in geophysical flows. Stratification changes the spatial turbulence spectrum and the energy transport and conversion within the spectrum. We analyze these effects based on a series of direct numerical simulations (DNS) of stratified turbulence.