Rayleigh-Taylor instability: experiments with image analysis

Rayleigh-Taylor instability is investigated in the laboratory using a simple apparatus of novel design to set up the unstable initial conditions. Visualisation techniques give a qualitative view of the development of the instability. Quantitative measurements are obtained through digital image analysis. Of primary interest is the evolution of the velocity field. Measurements are made over a two dimensional slice of the flow using an efficient, high-resolution particle tracking technique. This technique is described and its strengths and limitations are discussed in comparison with traditional measurement techniques. The visualisations and velocity measurements are compared with the experimental and numerical results of previous workers. 1. I N T R O D U C T I O N The Rayleigh-Taylor instability is relevant in fluid flows ranging from inertially confined fusion to adding milk to a cup of coffee. In the geophysical context there are a wide variety of mechanisms which may lead to the formation of an unstable density stratification, leading in turn to the development of the Rayleigh-Taylor instability, redistribution of the density, mixing, and ultimately stable stratification. An overview of the subject has been given by Sharp (1984). Analytical and numerical models of Rayleigh-Taylor (RT) instability generally utilise initial conditions which are in some sense ideal. Typically the fluid is at rest for times t < 0. At t = 0 the instability is switched on by imposing a destabilising acceleration such that the pressure and density gradients are in opposite directions. In the laboratory similar conditions may be obtained by accelerating an initially stable stratification downward at a rate exceeding the gravitational acceleration g. However, difficulties in instrumenting such experiments, the high cost of the experiments and their relatively short duration prevent such techniques being used in most 0377-0265 /93 /$06 .00 © 1993 Elsevier Science Publ ishers B.V. All r ights reserved 128 RAYLEIGH-TAYLOR INSTABILITY laboratories. Although in the geophysical context the initial conditions are seldom close to the ideal, there remains a strong argument for attempting to model and understand the ideal situation in the laboratory as this more readily lends insight to the basic physics of the flow. A variety of other methods have been employed to set up the unstable stratification. A common method (e.g. Voropayev et al., 1993) involves setting up a stable stratification (either layered or continuous) within a tank, then rapidly inverting the tank. This works reasonably well for very viscous fluids, but with inviscid fluids the body of the fluid remains irrotational during the inversion process. In a cylindrical tank rotated about its axis, the fluid would remain at rest with a stable stratification, whereas in a thin rectangular tank the density contours would finish at approximately 45 ° from the horizontal before the growth of the instability. Other methods rely on some form of barrier separating two homogeneous layers of different densities. The instability is then initiated by removing the barrier by rupturing a membrane, advecting the flow past it (splitter plate in stratified flume, e.g. Lawrence, personal communication, 1992), or simply pulling the barrier out (e.g. Linden and Redondo, 1991). The difficulty with these techniques arises primarily because it is not possible to remove the barrier without affecting the flow in some way: pieces of the ruptured membrane may be advected around by the flow, and the wake generated by the splitter plate or removal of the barrier may dominate the initial growth of the instability. For the present investigation a barrier is used to separate two homogeneous layers of (salt) water of equal depth but different density. The barrier is of a novel design originally suggested by Lane-Serif (1989, p. A7), which greatly reduces the wake and its effect on the development of the instability. Details of the barrier and experimental set-up may be found in Section 2. In Section 3 we present a number of visualisations of the developing instability, comparing them with analogous visualisations from a numerical code by Youngs (1991). The velocity measurements reported in this paper have been obtained by a particle tracking system developed by the author. The basic principles employed by this system are outlined in Section 4. A more comprehensive description has been given by Dalziel (1993). Although the system is capable of simultaneous density measurements (employing fluorescent dye as an indicator of density), this feature has not yet been used for the investigation of RT instability. 2. EXPERIMENTAL SETUP The experiments described in this paper were undertaken in a Perspex tank of 200 mm width, 400 mm length and 500 mm depth. This tank is