This project aims to develop a closure scheme for the atmospheric flow that is suitable for numerical truncation in the regime of stratified macro-turbulence. Particular emphasis is spent on conservation laws and scale invariance. High-resolution lidar and radar measurements of temperatures and winds, as well as retrievals from other methods, are used to construct horizontal and vertical wavenumber power spectra for the upper troposphere and the mesosphere, and to validate the model results.
Meso-scale energy cascades in the lower and middle atmosphere
My task is to extend the recently developed parameterization for friction/diffusion for atmospheric flows to the middle atmosphere.
Hi, I am Serhat from subproject T1. As a PhD candidate, my task is to extend the recently developed parameterization for friction/diffusion for atmospheric flows to the middle atmosphere, including full accounting of the spectral budget for kinetic and available potential energy. Complex flows cover a wide range of spatial and temporal scales and it becomes practically illogical to expect existing computational technology to simulate a realistic atmosphere for all observed phenomena. Thus, the emergence of accounting for the effects of unresolved scales is inevitable, resulting in what is known as the turbulence closure problem.
Closure is handled via the so-called Dynamic Smagorinsky Model (DSM), in the Kühlungsborn Mechanistic general Circulation Model (KMCM). This scheme eliminates ad hoc tuning for the parameterization and allows a space-time dependent mixing length, fully determined by the resolved flow.
Observational data from Nastrom & Gage point to transition from synoptic -3 slope to -5/3 in mesoscales for horizontal motion and temperature, providing a solid reference information for comparison. Atmosphere being strongly effected by gravity, anisotropic formulation is needed for DSM and the arguments of Stratified Macro Turbulence (SMT) comes into play for the aid, yielding an additional constraint on the dependence of vertical form of DSM on its horizontal part.
On top of all these intertwined descriptions of turbulence, scale invariance sets the tone and dictates equations to keep their forms unchanged for inertial regimes, including parameterizations. A dynamically determined mixing length complies with this requirement and definition of parameterization is completed. It should be emphasized that sub-grid scale motion is considered as a modelling of friction from a thermodynamic point of view. In this manner, only forward energy cascade with no backscatter must result on average from the spectral analyses of the circulation model.
Reasoning for a unidirectional energy cascade stems from the Lorenz Energy Cycle, where the conversions between kinetic, available and unavailable potential energy drives the climate. To appropriately represent this cycle detailed description of entropy production, i.e. friction due to motion is crucial. DSM appears as a comprehensive method to address above-mentioned demands in general circulation modelling. As a result, friction/diffusion in atmosphere represented in the framework of turbulence modelling creates an exciting meeting of seemingly distant fields.
Schaefer-Rolffs, U. (2018). The scale invariance criterion for geophysical fluids. European Journal of Mechanics-B/Fluids, Vol. 74, 92-98.
Schaefer-Rolffs, U. (2018). A comparison of different solutions for the Dynamic Smagorinsky Model applied in a GCM. Meteor. Z., 27, 249–261, doi:10.1127/metz/2018/0885
Vadas, S. L., Zhao, J., Chu, X., and E. Becker (2018). The excitation of secondary gravity waves from local body forces: Theory and observation.Journal of Geophysical Research: Atmospheres, 123(17), 9296-9325.
Schaefer-Rolffs, U. and Becker, E., (2018). Scale-invariant Formulation of Momentum Diffusion for High-Resolution Atmospheric Circulation Models , Monthly Weather Review, 146, 1045-1062, doi:10.1175/MWR-D-17-0216.1 .
Becker, E., and Vadas, S. L. (2018). Secondary Gravity Waves in the Winter Mesosphere: Results From a High‐Resolution Global Circulation Model. Journal of Geophysical Research: Atmospheres, 123(5), 2605-2627.