瑞利-泰勒不稳定性线性增长的密度梯度致稳

 研究了密度梯度对瑞利-泰勒不稳定性的致稳作用，采用有限元算法求解钱得拉塞卡方程本征值问题，得到不同密度分布下理想不可压流体力学量的扰动线性增长率及扰动速度分布。扰动增长率结果与修正的Lindl公式的计算结果比较发现：扰动分布的峰值位于密度梯度标长的取值位置处，波长与密度标长可比拟时，扰动增长率显著偏离Lindl公式，而长波和短波极限情况下，数值解和Lindl公式符合较好。

Variational approach for linear growth rate of Rayleigh-Taylor instability with continuous density profile

The stabilization effect on Rayleigh-Taylor instability of density gradient was studied, with the variational and finite element approach to solve the Chandrasekhar equation. The growth rates under different density profiles were gained for ideal incompressible fluids and compared with those derived by the modified Lindl formula. The largest difference between of the results the numerical simulation and the formula happens when the perturbation wave length equals to the density scale length, and the peak value of the perturbation lies at the points where the scale length function meets its extreme. The two results agree well when the pertubation wave number appoaches infinity or infinitesimal. The pertubation velocities were also got in the simulation.