Experimental study of Rayleigh–Taylor instability: Low Atwood number liquid systems with single-mode initial perturbations

Abstract

Single-mode Rayleigh–Taylor instability is experimentally studied in low Atwood number fluid systems. The fluids are contained in a tank that travels vertically on a linear rail system. A single-mode initial perturbation is given to the initially stably stratified interface by gently oscillating the tank in the horizontal direction to form standing internal waves. A weight and pulley system is used to accelerate the fluids downward in excess of the earth’s gravitational acceleration. Weight ranging from 90 to 450 kg produces body forces acting upward on the fluid system equivalent to those produced by a gravitational force of 0.33–1.35 times the earth’s gravity. Two fluid combinations are investigated: A miscible system consisting of a salt water solution and a water–alcohol solution; and an immiscible system consisting of a salt solution and heptane to which surfactant has been added to reduce the interfacial tension. The instability is visualized using planar laser-induced fluorescence and is recorded using a video camera that travels with the fluid system. The growth in amplitude of the instability is determined from the digital images and the body forces on the fluid system are measured using accelerometers mounted on the tank. Measurements of the initial growth rate are found to agree well with linear stability theory. The average of the late-time bubble and spike velocities is observed to be constant and described by Uave=0.22(πAG/k(1+A)+πAG/k(1−A)), where A is the Atwood number, k is the wave number, and G is the apparent gravity of the fluid system (i.e., the fluid system acceleration minus the earth’s gravity).