A Modeling Study of Nonstationary Trapped Mountain Lee Waves. Part I: Mean-Flow Variability

Abstract

The impact of mean-flow variability on finite-amplitude trapped mountain lee waves is investigated by conducting two-dimensional mountain wave simulations for a set of idealized, time-dependent background flows. The lee-wave patterns generated by these time-dependent flows depend on two factors: 1) the degree to which the transition in the background flow changes the amplitude of the stationary trapped lee wave and 2) the difference between the group velocities of the trapped waves generated before and after the transition. When the transition in the background flow significantly reduces the amplitude of the stationary lee wave, the lee-wave pattern generated prior to the transition gradually drifts downstream away from the mountain or back over the mountain, depending on the sign of this wave packet?s group velocity after the transition. When the transition in the background flow changes the resonant wavelength while leaving the lee-wave amplitude relatively unchanged, the lee-wave train develops either 1) a smooth transition in horizontal wavelength or 2) a region of irregular variations in wavelength and amplitude, depending on the difference between the group velocities of the waves generated before and after the transition. Although linear theory is able to predict how changes in the background flow will affect the group velocities of the trapped waves, it is not able to predict whether the temporal variations in the large-scale environmental flow will amplify or dampen the resonant waves when the waves are no longer linear. Regions of irregular variations in wavelength and amplitude may develop when stationary trapped waves generated after a transition in the background flow overtake the trapped waves generated before the transition. The fluctuations in the vertical velocities associated with such numerically simulated lee waves are compared with wind profiler observations. Estimates of the time required for the trapped waves generated after the transition to overtake those generated before the transition suggest that the temporal changes in the background flow required to qualitatively reproduce the observed vertical velocity variations are not likely to occur on a realistic timescale. In addition, the observed temporal variations in lee-wave vertical velocities appear to be the superposition of at least two distinct frequencies, whereas the temporal variations in the simulated waves are dominated by one distinct frequency.