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Numerical Simulations of Lee Wave's Nonlinear Characteristics and Vapor Sensitivity
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摘要: 从Scorer的背风波发生理论条件出发，首先考虑3层均匀干空气，利用WRF模式模拟出干空气条件下的小振幅拦截背风波动，波动主要发生在2~5 km的高度范围，波长为8 km左右，这与之前的观测和模拟结果相一致。分析表明：形成平稳背风波动过程中，存在能量波包向下游传播的性质，各位置振动的强度会发生周期性的增强和衰减。引入水汽进行的敏感性试验表明：随着水汽增多，背风波动的波长会增加，且波动传播中所能达到的最大垂直速度有变小趋势。Abstract:
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.
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Key words:
- lee wave;
- WRF model;
- nonlinear;
- vapor;
- numerical simulation
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图 2 干空气条件下第90分钟时流场 (流线) 和垂直速度 (阴影) 场分布
Fig. 2 Distribution of stream (streamline) and vertical velocity (shaded area) fields in dry air condition at the 90th minute
图 3 2~5 km高度的垂直速度平均场随时间变化
Fig. 3 Variation of vertical velocity mean field from 2 to 5 km
图 4 初始时刻空气相对湿度垂直分布廓线
Fig. 4 Profile of vertical distribution of the initial air relative humidity
图 5 积分60 min时不同水汽条件下背风波动的流场
Fig. 5 The stream of lee wave under various water vapor at the 60th minute of the simulations
图 6 不同水汽条件下3.5 km高度处的垂直速度
Fig. 6 Vertical velocity under various water vapor at the height of 3.5 km
表 1 数值试验中不同相对湿度空气发生对流的时间
Table 1 Initial convection time of simulations under various relative humidity
相对湿度/% 对流发生时间 50 第70分钟 60 第60分钟 70 第10分钟 90 第10分钟 
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