Numerical simulations of Hurricane Katrina (2005) in the turbulent gray zone

Current numerical simulations of tropical cyclones (TCs) use a horizontal grid spacing as small as Δx = 10³ m, with all boundary layer (BL) turbulence parameterized. Eventually, TC simulations can be conducted at Large Eddy Simulation (LES) resolution, which requires Δx to fall in the inertial subrange (often <10² m) to adequately resolve the large, energy-containing eddies. Between the two lies the so-called "terra incognita" because some of the assumptions used by mesoscale models and LES to treat BL turbulence are invalid. This study performs several 4-6 h simulations of Hurricane Katrina (2005) without a BL parameterization at extremely fine Δx [333, 200, and 111 m, hereafter "Large Eddy Permitting (LEP) runs"] and compares with mesoscale simulations with BL parameterizations (Δx = 3 km, 1 km, and 333 m, hereafter "PBL runs"). There are profound differences in the hurricane BL structure between the PBL and LEP runs: the former have a deeper inflow layer and secondary eyewall formation, whereas the latter have a shallow inflow layer without a secondary eyewall. Among the LEP runs, decreased Δx yields weaker subgrid-scale vertical momentum fluxes, but the sum of subgrid-scale and "grid-scale" fluxes remain similar. There is also evidence that the size of the prevalent BL eddies depends upon Δx, suggesting that convergence to true LES has not yet been reached. Nevertheless, the similarities in the storm-scale BL structure among the LEP runs indicate that the net effect of the BL on the rest of the hurricane may be somewhat independent of Δx.