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

Ultrasound Triggering of Rayleigh-Taylor Instability: Solution of Compressible Navier-Stokes Equation by a Non-Overlapping Parallel Compact Scheme

“…The Rayleigh-Taylor instability (RTI) [1,2] is present in different branches of physics, from hydrodynamic applications [3][4][5][6] to high energy physics of astrophysics [7,8] and nuclear confinement fusion [9,10]. Similarly, the baroclinic instability can arise during onset of RTI due to misalignment of density and pressure gradients, a major source of torque that contributes to the instability [11,12]. In the present research, the compressible flow formulation of the Navier-Stokes equation (NSE) in [12] has been used.…”

“…Similarly, the baroclinic instability can arise during onset of RTI due to misalignment of density and pressure gradients, a major source of torque that contributes to the instability [11,12]. In the present research, the compressible flow formulation of the Navier-Stokes equation (NSE) in [12] has been used. Such a formulation obviates the need of making the Boussinesq approximation, as needed for incompressible flow formulations.…”

“…The term given by, ω ∇ • V , is due to compressibility, and RTI should justifiably depend upon bulk viscosity as noted from the constitutive relation between stress and rates of strain tensors. Equation (1) demonstrates the need for predicting RTI using the compressible flow formulation along with the bulk viscosity contribution, as has been reported in [12,14], and the same formulation is also used here. Thus, without using the Stokes' hypothesis, the linear regression model for the bulk viscosity based on acoustic dispersion and attenuation experimental data of Ash et al [15] is utilized here also.…”

“…In Read's experiments [22], two geometrical setups were considered with the purpose of providing results for 2D and 3D flows. The present research aims to consider only the 3D RTI setup with A t = 0.5, while in [12], corresponding 2D and 3D setups were computed by solving the 3D geometry with cross-sections of (0.15m × 0.025m) and (0.15m × 0.15m), respectively.…”

“…In practice, there is no need to impose any length scale as there are many 2D and 3D direct numerical simulations (DNS) where the initial interface is purely taken as planar [12,14,20,21,27] to replicate the experiments reported in [17,22,28] where the fluid interface is initially plane and the onset of RTI has been shown to originate from the edges and corners of the initial interface [12].…”