Closing the Scale Gap for Resolved-Turbulence Simulations in Meteorology

Geophysical flow is generally characterized by huge Reynolds numbers—which limits our ability to directly represent these systems on a computer. Most practical applications such as weather forecasting or climate projection rely on the representation of small-scale processes, one of which is turbulent mixing, by parameterizations. Sometimes, however, an explicit representation is inevitable to further process-level understanding and allow for an informed representation of mixing processes in parameterizations. While an explicit representation of turbulence is not possible across the entire geophysical range of scales, hydrodynamic/Reynolds-number similarity can be exploited to quantitatively extrapolate the behavior at reduced scale to the geophysically relevant limit of large scale separation. We outline here the underlying methodological framework and illustrate the approach by two examples, namely a general formulation of the velocity profiles in Ekman flow and the explicit representation of roughness in a channel flow resembling a boundary layer modeled in a wind tunnel.