1st Leibniz MMS Days - Abstract
Becker, Erich
Fostered by the increase in computer capabilities, global climate models have undergone considerable developments towards including more processes and increased resolutions. Nevertheless, the representation of unresolved dynamical scales by subgrid-scale schemes is still an issue, even in idealized model configurations. Typically, the parameters of subgrid-scale schemes must be chosen in dependence on the actual numerical resolution, i.e., the numerical solutions of the (partly empirical) equations of motion do not converge. In this contribution we use a primitive equation model that is based on the spectral transform method and equipped with an anisotropic Smagorinsky scheme. We demonstrate that the global kinetic spectrum in the free troposphere, which shows a kink toward a -5/3 exponential slope in the mesoscale, can only be simulated when the Smagorinsky scheme is completed by some hyperdiffusion. However, any hyperdiffusion cannot be reconciled with the second law of thermodynamics. Assuming that the mesoscales in the free troposphere are subject to a macro-turbulent inertial range that fulfills the scaling laws of stratified turbulence (ST), a scale-invariant version of the Smagorinsky scheme (so-called Dynamic Smagorinsky Model, DSM) has been developed and applied to horizontal momentum diffusion. We show that the constraint of scale-invariance combined with the scaling laws of (ST) allows to compute also the vertical mixing in dependence on the horizontal mixing length. Furthermore, the new DSM automatically yields the mixing lengths for sensible heat and tracers. We present test simulations in order to validate the new DSM with regard to its ability to simulate the -5/3 exponential slope of the global energy spectrum without invoking non-physical or artificial measures.