A Modeling Study of Nonstationary Trapped Mountain Lee Waves. Part II: Nonlinearity

Abstract

The generation of nonstationary trapped mountain lee waves through nonlinear wave dynamics without any concomitant change in the background flow is investigated by conducting two-dimensional mountain wave simulations. These simulations demonstrate that finite-amplitude lee-wave patterns can exhibit temporal variations in local wavelength and amplitude, even when the background flow is perfectly steady. For moderate amplitudes, a nonlinear wave interaction involving the stationary trapped wave and a pair of nonstationary waves appears to be responsible for the development of nonstationary perturbations on the stationary trapped wave. This pair of nonstationary waves consists of a trapped wave and a vertically propagating wave, both having horizontal wavelengths approximately twice that of the stationary trapped wave. As the flow becomes more nonlinear, the nonstationary perturbations involve a wider spectrum of horizontal wavelengths and may dominate the overall wave pattern at wave amplitudes significantly below the threshold required to produce wave breaking. Sensitivity tests in which the wave propagation characteristics of the basic state are modified without changing the horizontal wavelength of the stationary trapped wave indicate these nonstationary perturbations are absent when the background flow does not support nonstationary trapped waves with horizontal wavelengths approximately twice that of the stationary trapped mode. These sensitivity tests also show that a second nonstationary trapped wave can assume the role of the nonstationary vertically propagating wave when the Scorer parameter in the upper layer is reduced below the threshold that will support the vertically propagating wave. In this case, a resonant triad composed of three trapped waves appears to be responsible for the development of nonstationary perturbations. The simulations suggest that strongly nonlinear wave dynamics can generate a wider range of nonstationary trapped modes than that produced by temporal variations in the background flow. It is suggested that the irregular variations in lee-wave wavelength and amplitude observed in real atmospheric flows and the complex fluctuations above a fixed point that are occasionally found in wind profiler observations of trapped lee waves are more likely to be generated by nonlinear wave dynamics than changes in the background flow.