Role of non-zero bulk viscosity in three-dimensional Rayleigh-Taylor instability: Beyond Stokes’ hypothesis

Abstract

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.