The impact of atmospheric boundary layer (ABL) interactions with large scale stably-stratified flow over an isolated, two-dimensional hill is investigated using turbulence resolving large-eddy simulations across a range of classical inverse Froude number, Fr-1 = Nh/Ug. We find that an alternative choice in the characteristic vertical length scale such as Frc-1= N(h-zi)/Ug, where zi is the ABL height, better captures both the onset of internal gravity wave, (IGW)-breaking and lee-side flow response regime. It is shown via energy spectra, that the onset of the nonlinear-breakdown regime, Frc-1 ~1.0, is initiated when IGW vertical wavelength becomes comparable to scales of sufficiently energetic turbulence in the stagnation zone and ABL. These spectra support the notion of an abrupt transition in lee-side flow response regime, and illustrate two distinct turbulent kinetic energy distribution states for the trapped-lee-wave and the nonlinear-breakdown regimes. In addition, we use these LES model results to investigate the role and accuracy of one-dimensional planetary boundary layer (PBL) parameterizations commonly used in mesoscale models.
Mesoscale simulations utilizing four one-dimensional PBL parameterizations result overall in reasonable agreement with the LES results for vertical wavelength, velocity amplitude, and turbulent kinetic energy distribution in the region of downhill shooting flow. Yet, the assumption of horizontal homogeneity in PBL parameterizations does not hold in the context of these complex flow configurations, resulting in a vertical wavelength shift producing errors of ~10 ms-1 at locations farther downstream due to the presence of a coherent trapped lee wave that does not mix with the atmospheric boundary layer. This effort, despite the simplicity of the terrain considered, illustrates the need for development of three-dimensional PBL schemes to improve mesoscale predictions in complex-terrain and other types of flows where one-dimensional PBL assumptions are violated.