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

Abstract

Rayleigh-Taylor instability (RTI) occurs at the interface of two media when the heavier fluid is accelerated into the lighter fluid and is a prototypical hydrodynamic event present in many physical events. In high energy physics, this manifests itself across a wide range of length scales from nuclear confinement fusion at micron-scale to supernova explosion at terra scales. RTI can also be viewed as a baroclinic instability prevalent in engineering, geophysics, and astrophysics, a pedagogic description of which is given in Sengupta et al., Comput. Fluids, 225, 104995 (2021) with respect to the experimental results of Read, Physica D, 12 45-58 (1984). Here, a recently proposed non-overlapping parallel algorithm is used to solve this three-dimensional canonical problem, having the unique property of not distinguishing between sequential and parallel computing, using 4.19 billion points and a refined time step of 7.69 × 10 −8 sec. The problem achieves the required density gradient by considering two volumes of air at different temperatures (with a temperature difference of 200K) separated by a non-conducting, impermeable partition at the onset of the experiment, which is removed impulsively at t = 0. The resulting buoyancy force at the interface acting from top to bottom is the seed of the baroclinic instability. Present high precision computation enables one to capture the ensuing RTI triggered by ultrasonic waves created at the interface.