Rarefaction-driven Rayleigh–Taylor instability. Part 1. Diffuse-interface linear stability measurements and theory

Abstract

Theory and experiments are reported that explore the behaviour of the RayleighTaylor instability initiated with a diffuse interface. Experiments are performed in which an interface between two gases of differing density is made unstable by acceleration generated by a rarefaction wave. Well-controlled, diffuse, two-dimensional and three-dimensional, single-mode perturbations are generated by oscillating the gases either side to side, or vertically for the three-dimensional perturbations. The puncturing of a diaphragm separating a vacuum tank beneath the test section generates a rarefaction wave that travels upwards and accelerates the interface downwards. This rarefaction wave generates a large, but non-constant, acceleration of the order of 1000g 0 , where g 0 is the acceleration due to gravity. Initial interface thicknesses are measured using a Rayleigh scattering diagnostic and the instability is visualized using planar laser-induced Mie scattering. Growth rates agree well with theoretical values, and with the inviscid, dynamic diffusion model of Duff et al. (Phys. Fluids, vol. 5, 1962, pp. 417-425) when diffusion thickness is accounted for, and the acceleration is weighted using inviscid Rayleigh-Taylor theory. The linear stability formulation of Chandrasekhar (Proc. Camb. Phil. Soc., vol. 51, 1955, pp. 162-178) is solved numerically with an error function diffusion profile using the Riccati method. This technique exhibits good agreement with the dynamic diffusion model of Duff et al. for small wavenumbers, but produces larger growth rates for large-wavenumber perturbations. Asymptotic analysis shows a 1/k 2 decay in growth rates as k → ∞ for large-wavenumber perturbations.

The effect of initial conditions on mixing transition of the Richtmyer–Meshkov instability

“…Here, ψ represented a growth reduction factor which increases with interface thickness having values of ψ = 1 for a discontinuous interface and ψ > 1 for a continuous interface. Duff et al's inviscid dynamic diffusion model provided reasonable agreement with their experiments and has compared favourably with the measurements of Morgan et al (2016). Brouillette & Sturtevant (1994) used Richtmyer's formulation of Taylor's theory to extend Duff et al's (1962) model for the case of an impulsively accelerated diffuse interface instability givinġ…”

“…In addition, the RT instability begins developing immediately as soon as the two gases (if the heavier one is above) come into contact when the plate begins sliding out (Puranik et al 2004). The interface produced in this manner is very diffuse (>1 cm) which can reduce the RM instability growth rate significantly (Mikaelian 1991;Jones & Jacobs 1997;Collins & Jacobs 2002;Morgan, Likhachev & Jacobs 2016). While Puranik et al's (2004) study was the only work to use a sinusoidally shaped plate, the initial perturbation induced in earlier studies was solely dependent on the disturbance created by the sliding motion of the flat plate.…”

Rayleigh-Taylor Instability: A Status Review of Experimental Designs and Measurement Diagnostics

“…An experimental facility that uses rarefaction waves to drive RTI has been developed recently at the U. Arizona (see Fig. 4(b)) [58,59] (henceforth referred to as RW). Similar in principle to the experimental design of Lewis, a diaphragm separates a vacuum tank beneath the test section; the diaphragm is ruptured to generate a rarefaction wave that travels outward and accelerates the interface downwards (see Fig.…”

Experiments and Simulations on the Turbulent, Rarefaction Wave Driven Rayleigh–Taylor Instability

“…The top of the reflection section is enclosed with a flange, where a 76 mm diameter fused silica window and two gas inlets are attached. More detail regarding the experimental apparatus can be found in the 2016 and 2018 papers by Morgan et al [27][28][29].…”

“…This image shows the vacuum tank at the bottom of the apparatus, the test section in the middle, and the bottom of the reflection section at the top. (Reproduced with permission from Ref [28]…”