O the Relative Importance of Nonlinearity and Mean Flow Variability in the Generation of Nonstationary Trapped Mountain Lee Waves.

A number of observational studies over the past three decades have noted that trapped mountain lee waves can undergo substantial structural changes on time scales as short as an hour. These structural changes range from smooth wavelength transitions to more complex transitions with wave patterns of highly variable wavelength and amplitude. Nonstationary trapped-lee waves are often viewed as a linear phenomenon resulting from temporal variations in upstream flow. Our work with nonlinear numerical simulations of steady flow over topography has revealed that nonstationary trapped -lee waves can be generated by nonlinearity. This study assesses the relative importance of nonlinearity and mean flow variability in the generation of nonstationary trapped -lee waves by comparing the time-dependent behavior in two -dimensional numerical simulations of finite-amplitude trapped -lee waves forced by steady and time-dependent flows. Numerical simulations for moderate mountain heights and steady upstream flow based on simple layered structures and observational profiles indicate that, under certain circumstances, nonlinear effects can transfer energy from the stationary trapped mode to nonstationary trapped modes with a wavenumber that is approximately half that of the stationary trapped mode. The superposition of the stationary and nonstationary trapped waves produces an oscillatory trapped-lee wave pattern whose peaks and troughs trace elliptical paths. The oscillations of neighboring peaks and troughs are out of phase, creating a trapped-lee wave pattern with highly variable wavelength and amplitude. Vertical wind shear in the background flow accelerates the breakdown of the stationary trapped wave, increasing the complexity of the trapped-lee wave pattern. When the background flow does not support a subharmonic trapped mode, the flow generates stationary finite-amplitude trapped-lee waves. The overall appearance of trapped-lee wave patterns generated by time-dependent flows based on horizontally -uniform, static-stability transitions depends on two basic factors: (1) the amplitude tendency, and (2) the downstream gradient in the horizontal group velocity. For some time -dependent flows, the amplitude variation is large enough that the generation of the trapped-lee wave appears to cease after the mean flow transition. Due to a profile dependence of the nonlinear amplification process, linear theory is unable to predict this amplitude tendency. When the mean flow variability does not produce a large amplitude variation, this type of time-dependent flow can generate either smooth wavelength transitions or complex highly time-dependent wave patterns. If the horizontal group velocity associated with the trapped waves increases downstream, then the trapped-lee wave pattern is characterized by a smooth wavelength transition. If the horizontal group velocity decreases downstream, the trapped-lee wave pattern is characterized by highly variable wavelength and amplitude. The response of the trapped waves to this type of basic state transition is such that linear theory is able to predict which type of wave pattern (smooth vs. complex) the time -dependent flow will generate.