Three-dimensional direct numerical simulations (DNS) of Rayleigh-Taylor instability (RTI) at the interface of two masses of air with a sharp temperature gradient of 149 K are performed by solving the compressible Navier-Stokes equation (NSE). The flow is studied in an isolated box with non-periodic walls along the three directions. A non-conducting interface separating the two air masses is impulsively removed at the onset of the instability. No external perturbation has been used at the interface to instigate the instability at the onset, corresponding to practical scenarios in experiments. Computations have been carried out for the two configurations reported by Read (Experimental investigation of turbulent mixing by Rayleigh-Taylor instability, Physica D. 12, 45–58 (1984)). The compressible formulation is free from the Boussinesq approximation commonly used for solving the incompressible NSE. The role of non-zero bulk viscosity is quantified by using a model from acoustic attenuation measurements for the bulk viscosity of air. Effects of Stokes’ hypothesis on the onset of RTI and the growth of mixing layer are reported. The incipient stage is shown to have a strong dependence on the constitutive relation used. The small-scale billowing motion is only observed for non-zero bulk viscosities. Following this stage, the growth rates for bubbles and spikes in the mixing layer are found to be underpredicted by 12% with the use of Stokes’ hypothesis. The results imply that the evolution of RTI from the onset to the fully turbulent regime is best captured by using non-zero values of the bulk viscosity.

通过求解可压缩的Navier-Stokes方程（NSE），进行了两个空气质量为149 K的急剧梯度的瑞利-泰勒不稳定性（RTI）的三维直接数值模拟（DNS）。在一个隔离的盒子中研究流动，该盒子具有沿三个方向的非周期性壁。在不稳定性开始时，将两个空气团分开的非导电界面被冲掉。与实验中的实际情况相对应，没有在界面处使用外部干扰来引发不稳定性。已对Read报道的两种配置进行了计算（由Rayleigh-Taylor不稳定性进行的湍流混合实验研究，Physica D. 12，45-58（1984））。可压缩配方没有通常用于求解不可压缩NSE的Boussinesq近似。非零体积粘度的作用通过使用声学衰减测量模型对空气的体积粘度进行量化。报道了斯托克斯假说对RTI发作和混合层生长的影响。初始阶段显示出对所使用的本构关系有很强的依赖性。仅在非零体积粘度下观察到小范围的滚滚运动。在此阶段之后，使用斯托克斯假设，发现混合层中气泡和尖峰的增长率被低估了12％。结果表明，通过使用非零值的本体粘度，可以最好地捕获RTI从开始到完全湍流状态的演变。