Experimental study of incompressible Richtmyer–Meshkov instability

Abstract

The Richtmyer-Meshkov instability of a two-liquid system is investigated experimentally. These experiments utilize a novel technique that circumvents many of the experimental difficulties that have previously limited the study of Richtmyer-Meshkov instability. The instability is generated by vertically accelerating a tank containing two stratified liquids by bouncing it off of a fixed coil spring. A controlled two-dimensional sinusoidal initial shape is given to the interface by oscillating the container in the horizontal direction to produce standing waves. The motion of the interface is recorded during the experiments using standard video photography. Instability growth rates are measured and compared with existing linear theory. Disagreement between measured growth rates and the theory are accredited to the finite bounce length. When the linear stability theory is modified to account for an acceleration pulse of finite duration, much better agreement is attained. Late time growth curves of many different experiments seem to collapse to a single curve when correlated with the circulation deposited by the impulsive acceleration. A theory based on modeling the late time evolution of the instability using a row of vortices is developed. The growth curve given by this model has similar shape to those measured, but underestimates the late-time growth rate.

Richtmyer–Meshkov instability: theory of linear and nonlinear evolution

“…Figure 13 shows the temporal evolution of an interface for Atwood number A = 0.155, and initial amplitude a 0 = 0.2 over the normalized time 0 ≤ t ≤ 9.4. This corrugation amplitude, the Atwood number, the time and the regularized parameter d (d = 0.15 here) are chosen so that the numerical computations are directly comparable with the experiment by Jacobs & Sheeley (1996). a 0 = 0.2 corresponds to the interface perturbation amplitude when a tank was detached from a coil spring in the experiment 0.3 cm in a real scale.…”

“…It can either be initially deposited or supplied by external sources, and the initially deposited vorticity can be affected by the rippled shock(s) through sound waves. A good example of vorticity deposited at the interface is the interfacial instability between immiscible fluids driven by a free-falling tank bouncing off a fixed spring for a short interval (Jacobs & Sheeley 1996). They give a sinusoidal interface perturbation, for example x 0 cos(kx), between two fluids in the tank, using novel experimental techniques.…”

“…Zabusky et al visualized its complex dynamics with the use of hydrodynamic simulations, and coined the terms 'vortex paradigm' and 'vortex projectile' (Hawley & Zabusky 1989;Zabusky & Zeng 1998;Zabusky 1999;Zabusky & Zhang 2002). In tank experiments (Jacobs & Sheeley 1996), they also visualized complex dynamics of the interface, such as the spiral structure of a spike. It should, however, be mentioned that in this review we consider only sinusoidal perturbations as initial interface corrugations and exclude subsequent turbulent regimes often observed in shock tube experiments (Houas & Chemouni 1996;Poggi et al 1998).…”

Computing multi-mode shock-induced compressible turbulent mixing at late times

“…Instead of using the classic shocktube, the authors impulsively accelerated a box containing the fluids by allowing it to fall onto a cushioned surface. The technique was successively improved by using coils instead of cushions by Jacobs and Sheeley (1996). Jones and Jacobs (1997) generated the interface between two fluids without using any solid membrane, which was until then the standard approach but introduced experimental uncertainties, e.g.…”

Experimental investigation of cylindrical converging shock waves interacting with a polygonal heavy gas cylinder

“…In the case of a planar shock, different techniques developed to form the initial interfaces have been reported in the literature. Typically, the interfaces of different shapes between two gases include spherical bubbles formed by a soap film (Haas & Sturtevant 1987;Layes, Jourdan & Houas 2003;Ranjan et al 2005;Zhai et al 2011;Si et al 2012), circular gas cylinders (Haas & Sturtevant 1987;Hosseini & Takayama 2005;Tomkins et al 2008;Luo et al 2014b), elliptical gas cylinders On converging shock and polygonal interface interaction 227 (Zou et al 2010), single-/multi-mode interfaces generated by vibration (Jacobs & Sheeley 1995;Mariani et al 2008;Long et al 2009) or by a gas curtain (Balakumar et al 2008;Orlicz et al 2009;Balasubramanian et al 2012), rectangular blocks generated by a microfilm membrane supported by a fine wire mesh (Bates, Nikiforakis & Holder 2007), and three-dimensional interfaces with a minimum surface feature formed by the soap film technique free of supporting meshes . Recently, some polygonal interfaces have been formed in our group using thin pins to restrict the soap film and the results indicate that the soap film is a flimsy but durable material during the interface formation Zhai et al 2014;Luo et al 2015).…”