Incompressible Miscible Experiments on the Two-Layer and Three-Layer Rayleigh-Taylor Instability

Abstract

Incompressible miscible Rayleigh-Taylor instability experiments are presented in which combinations of two and three stratified liquids, in an initially stable configuration of increasing density from top to bottom, having Atwood number of 0.56 between the top and bottom fluids for all cases and 0.31 across each interface for the three-layer cases are accelerated in a vertical linear induction motor (LIM) drop tower. Isopropyl alcohol and LST Heavy Liquid (a concentrated solution of lithium heteropolytungstates in water) comprise the top and bottom layers, with a dilution of LST in water used for the intermediate density middle layer for three-layer experiments. A test sled containing the experimental fluid tank and visualization equipment is positioned at the top of the tower and parametrically forced to produce an initial perturbation, then accelerated downward by the LIMs causing the initially stable interface to be destabilized, allowing the Rayleigh-Taylor instability to develop. A backlight is used to illuminate the fluid tank which is viewed by a monochromatic high-speed camera that images the growing mixing region over the course of an experiment. Mixing region width, rate of growth, and growth constant are compared between two-layer and three-layer experiments with middle layer thicknesses of 0.5 and 0.75 cm. Inclusion of an intermediate layer is observed to delay growth of the mixing region, but the thickness of the layer has no noticeable impact on this delay for the thicknesses used. The middle layer is additionally observed to suppress growth, with a stronger affect resulting from a greater thickness. Late time rates of growth of the overall mixing region plateau at 1.17~$\pm$~0.27~$\frac{mm}{ms}$ and 0.75~$\pm$~0.13~$\frac{mm}{ms}$ for middle layer thicknesses of 0.5~cm and 0.75~cm respectively. Two-layer experiments progress past the view of the camera before this plateauing is observed. Calculations of the growth constant display similar trends, with late-time values of $\alpha=0.070\pm0.035$ (for 0.5~cm) and $\alpha=0.025\pm0.008$ (for 0.75~cm) calculated using the half-width of the overall mixing region. Two-layer experiments again develop too quickly for this to be observed. Spike and bubble growth constants are also found individually, calculated to be $\alpha_s=0.091\pm0.059$ and $\alpha_b=0.087\pm0.038$ for the 0.5~cm experiments and $\alpha_s=0.020\pm0.004$ and $\alpha_b=0.047\pm0.018$ for the 0.75~cm experiments. Statistical analysis indicates a difference between these late-time values for the different middle layer thicknesses at a confidence level of 95\%, with the exclusion of bubble values, which only satisfy a 90\% confidence level.