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- ItemA scale invariance criterion for les parametrizations(Stuttgart : Gebrüder Bornträger Verlagsbuchhandlung, 2014) Schaefer-Rolffs, U.; Knöpfel, R.; Becker, E.Turbulent kinetic energy cascades in fluid dynamical systems are usually characterized by scale invariance. However, representations of subgrid scales in large eddy simulations do not necessarily fulfill this constraint. So far, scale invariance has been considered in the context of isotropic, incompressible, and three-dimensional turbulence. In the present paper, the theory is extended to compressible flows that obey the hydrostatic approximation, as well as to corresponding subgrid-scale parametrizations. A criterion is presented to check if the symmetries of the governing equations are correctly translated into the equations used in numerical models. By applying scaling transformations to the model equations, relations between the scaling factors are obtained by demanding that the mathematical structure of the equations does not change. The criterion is validated by recovering the breakdown of scale invariance in the classical Smagorinsky model and confirming scale invariance for the Dynamic Smagorinsky Model. The criterion also shows that the compressible continuity equation is intrinsically scale-invariant. The criterion also proves that a scaleinvariant turbulent kinetic energy equation or a scale-invariant equation of motion for a passive tracer is obtained only with a dynamic mixing length. For large-scale atmospheric flows governed by the hydrostatic balance the energy cascade is due to horizontal advection and the vertical length scale exhibits a scaling behaviour that is different from that derived for horizontal length scales.
- ItemEnhanced gravity-wave activity and interhemispheric coupling during the MaCWAVE/MIDAS northern summer program 2002(München : European Geopyhsical Union, 2006) Becker, E.; Fritts, D.C.We present new sensitivity experiments that link observed anomalies of the mesosphere and lower thermosphere at high latitudes during the MaCWAVE/MIDAS summer program 2002 to enhanced planetary Rossby-wave activity in the austral winter troposphere. We employ the same general concept of a GCM having simplified representations of radiative and latent heating as in a previous study by Becker et al. (2004). In the present version, however, the model includes no gravity wave (GW) parameterization. Instead we employ a high vertical and a moderate horizontal resolution in order to describe GW effects explicitly. This is supported by advanced, nonlinear momentum diffusion schemes that allow for a self-consistent generation of inertia and mid-frequency GWs in the lower atmosphere, their vertical propagation into the mesosphere and lower thermosphere, and their subsequent dissipation which is induced by prescribed horizontal and vertical mixing lengths as functions of height. The main anomalies in northern summer 2002 consist of higher temperatures than usual above 82 km, an anomalous eastward mean zonal wind between 70 and 90 km, an altered meridional flow, enhanced turbulent dissipation below 80 km, and enhanced temperature variations associated with GWs. These signals are all reasonably described by differences between two long-integration perpetual model runs, one with normal July conditions, and another run with modified latent heating in the tropics and Southern Hemisphere to mimic conditions that correspond to the unusual austral winter 2002. The model response to the enhanced winter hemisphere Rossby-wave activity has resulted in both an interhemispheric coupling through a downward shift of the GW-driven branch of the residual circulation and an increased GW activity at high summer latitudes. Thus a quantitative explanation of the dynamical state of the northern mesosphere and lower thermosphere during June-August 2002 requires an enhanced Lorenz energy cycle and correspondingly enhanced GW sources in the troposphere, which in the model show up in both hemispheres.