Momentum Fluxes of Gravity Waves Generated by Variable Froude Number Flow over Three-Dimensional Obstacles

Fully nonlinear mesoscale model simulations are used to investigate the momentum fluxes of gravity waves that emerge at a "far-field" height of 6 km from steady unsheared flow over both an axisymmetric and elliptical obstacle for nondimensional mountain heights (h) over cap (m) = Fr-1 in the range 0.1-5, where Fr is the surface Froude number. Fourier- and Hilbert-transform diagnostics of model output yield local estimates of phase-averaged momentum flux, while area integrals of momentum flux quantify the amount of surface pressure drag that translates into far-field gravity waves, referred to here as the "wave drag" component. Estimates of surface and wave drag are compared to parameterization predictions and theory. Surface dynamics transition from linear to high-drag (wave breaking) states at critical inverse Froude numbers Fr-c(-1) predicted to within 10% by transform relations. Wave drag peaks at Fr-c(-1) < <(h)over cap>(m) less than or similar to 2, where for the elliptical obstacle both surface and wave drag vacillate owing to cyclical buildup and breakdown of waves. For the axisymmetric obstacle, this occurs only at (h) over cap (m) = 1.2. At (h) over cap (m) greater than or similar to 2-3 vacillation abates and normalized pressure drag assumes a common normalized form for both obstacles that varies approximately as (h) over cap (-1.3)(m). Wave drag in this range asymptotes to a constant absolute value that, despite its theoretical shortcomings, is predicted to within 10%-40% by an analytical relation based on linear clipped-obstacle drag for a Sheppard-based prediction of dividing streamline height. Constant wave drag at (h) over cap (m) similar to 2-5 arises despite large variations with (h) over cap (m) in the three-dimensional morphology of the local wave momentum fluxes. Specific implications of these results for the parameterization of subgrid-scale orographic drag in global climate and weather models are discussed.