Numerical Simulations of Lee Wave's Nonlinear Characteristics and Vapor Sensitivity

Based on the Scorer's theory of the lee wave, the trapped lee wave of small amplitude is successfully simulated using the Weather Research and Forecasting (WRF) model, considering the dry atmosphere with three even layers. Results show that in the linear theory, the trapped lee wave of the flow over terrain can be simulated well. The wave appears primarily from 2 km to 5 km in the vertical direction and the wavelength is on the order of 8 km. These results are in accordance with previous observation and numerical simulations.The analysis shows that the energy wave packet drifts downstream in the forming process of stationary lee wave and the oscillation intensity of each location periodically amplifies and weakens. At the same time, before the stable trapped lee wave forms, small disturbances have been generated, which would have significant impacts on vertical velocity of the wave.The process of introducing vapor is deemed to be creditable according to the original relative humidity vertical profile by WRF model output data. Small disturbances mentioned make vapor oscillate and easily initiate cumulus convection. Further, with vapor content increasing, cumulus convection appears earlier in the simulation. When vapor is introduced in the model, the lee wave would interact with cumulus convection, which has not been discussed in detail.Sensitivity experiments are conducted by changing the relative humidity of air, and the simulated results about the vapor's effect to the lee wave show that as the vapor increases, the wavelength becomes longer. In the simulation, the wavelength increases from 8 km to 9 km when relative humidity increases from 0 to 60%. In essence, it is buoyancy oscillation in the vertical direction of lee wave. The increase of the turbulent friction is attributed to the air density changes because of the variation of humidity, and then the damp of the oscillation increases. As a result, the oscillation frequency in the moist air is smaller than that in the dry air, accordingly the lee wave shifts to longer wavelength.Besides, when vapor is introduced in the model, the maximum of vertical velocity in the process of wave propagation has a decreasing tendency. For one thing, the strength of the lee wave can be weakened by the growth of turbulent friction. On the other hand, the vertical velocity will decrease with the air density increasing for the same wave energy.