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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.
- ItemDeviations from a general nonlinear wind balance: Local and zonal-mean perspectives(Stuttgart : Gebrüder Bornträger Verlagsbuchhandlung, 2014) Gassmann, A.The paper introduces the active wind as the deviation from a general local wind balance, the inactive wind. The inactive wind is directed along intersection lines of Bernoulli function and potential temperature surfaces. In climatological steady state, the inactive mass flux cannot participate in net-mass fluxes, because the mean position of the mentioned intersection lines does not change. A conceptual proximity of the zonal-mean active wind to the residual wind as occurring in the transformed Eulerian mean equations suggests itself. The zonaland time-mean active wind is compared to the residual wind for the Held-Suarez test case. Similarities occur for the meridional components in the zone of Rossby wave breaking in the upper troposphere equatorward of the jet. The vertical components are similar, too. However, the vertical active wind is much stronger in the baroclinic zone. This is due to the missing vertical eddy flux of Ertel's potential vorticity (EPV) in the TEM equations. The largest differences are to be found in the boundary layer, where the active wind exhibits typical pattern of Ekman dynamics. Instantaneous active wind vectors demonstrate mass-inflow for lows and mass-outflow for highs in the boundary layer. An active meridional wind is associated with a filamentation of EPV in the zone of Rossby wave breaking in about 300 hPa. Strong gradients of EPV act as a transport barrier.