大气湍流引起飞机颠簸的理论分析和数值试验

Numerical Simulation and Dynamical Analysis of Atmospheric Turbulence Influence on the Aircraft Bumps

基于飞机载荷因数变量方程、无量纲的大气垂直运动方程和热力学方程,建立起描述大气湍流和飞机颠簸的湍流模型,并对该模型进行理论分析和数值试验。研究指出,负的理查森数(Ri)对应着静力不稳定和动力不稳定流动,在不稳定大气层结条件下,当Ri<-Ra/PrRe2时,对流状态的大气运动必将由对流转变成湍流,并对运行于其中的飞机产生飞机颠簸。但在稳定大气层结条件下,当理查森数大于临界理查森数时〔Ri>Ric=-Ra/PrRe2〕,正的Richardson数是动力稳定的,非对流状态的大气运动表现为重力波。当理查森数小于临界理查森数〔0<Ri<Ric=-Ra/PrRe2〕时,即存在1个小区0<Ri<Ric,在这里正的理查森数是动力不稳定的,大气运动表现为非周期性的湍流随机运动。非对流状态的大气运动因重力波不稳定碎变为湍流,将产生晴空湍流和晴空飞机颠簸。

Based on the aircraft loading coefficient variable equation, which is obtained from the equation of aircraft dynamics, the aircraft bumps are studied. The results show that the aircraft bumps are mainly determined on the vertical wind velocity of the flow. The mathematical model of atmospheric turbulence and aircraft bumps is derived from the vertical motion equation and the thermodynamic equation, which is based on the non- dimensional Navier-stokes equations. Numerical simulation of the model show that gravity waves may be dynamically unstable and lead to breaking and becoming turbulence. Under the small positive Richardson number and the big Reynolds number conditions, non-periodic solutions in the vertical direction are obtained from the model. However, under the small Reynolds number conditions, non-periodic flow must occur ＇as time increases. In addition, Lorenz equation representing cellular convection is derived from the model and solved numerically, and the solutions of Lorenz equation are found to be unstable and the non-periodic flow can be found.