Rayleigh–Taylor instability in complex stratifications

Abstract

The Rayleigh–Taylor instability of a system of three fluids separated by one unstable and one stable interface has been investigated experimentally. The experiments were gravitationally driven and conducted with miscible liquids consisting of salt solutions and fresh water. The lower two layers are initially gravitationally stable and are formed by depositing the lighter fluid on top of a thicker layer of the heavier one. The relatively thick top layer is initially separated from the two lower layers by a rigid barrier that is removed at the start of an experiment. In situations where the density of the bottom-layer fluid equals that of the top-layer fluid, the resulting turbulent flow is found to be self-similar as demonstrated by the collapse of the mean concentration distributions as well as the behaviour of the decay of the peak of the mean concentration profiles. In this configuration, the erosion of the bottom layer by the turbulence generated by the upper unstable interface is found to be small. When the density of the bottom-layer fluid is increased above that of the top-layer fluid, the degree of erosion is further decreased. In the cases where the lower interface is stably stratified at late-time, the entrainment rate E at the lower (statically stable) interface is found to follow a power law of the Richardson number, i.e. $E \propto Ri^{-n}$, with $n {\approx} 1.3$, a result in agreement with studies of mixing induced by oscillating grids. When the density of the bottom-layer fluid is decreased below that of the top-layer fluid, the erosion increases as expected. However, in this case, the overall density distribution is such that it is globally Rayleigh–Taylor unstable at late time. In this situation, the turbulent mixing region at late times grows similarly to that of single-interface Rayleigh–Taylor instability with approximately the same value of the growth constant. In these late-time unstable experiments the density profile approaches that of an equivalent two-layer Rayleigh–Taylor unstable system.