Effect of shear on Rayleigh-Taylor mixing at small Atwood number

Abstract

The effect of shear on the development of Rayleigh-Taylor instability (RTI) is studied at an Atwood number of 0.035 using the gas tunnel at Texas A University. Two types of diagnostics, imaging and simultaneous hot wire and cold wire anemometry, are used to measure mix widths, pointwise instantaneous velocities, and density. Image analysis has shown that the superposition of shear on RTI development increases the mixing width and growth rate at early times ($\ensuremath{\tau}=\frac{x}{U}\sqrt{\frac{{A}_{t}g}{H}}\ensuremath{\ll}1$). In particular, the mixing region shows distinct characteristics of shear (Kelvin-Helmholtz instability) and buoyancy (RTI). The Kelvin-Helmholtz (KHI) instability is observed to be dominant at early times, and the RTI at late times ($\ensuremath{\tau}1$). In the late-time self-similar regime ($\ensuremath{\tau}1$), the mix width growth rate coefficient obtained using digital image analysis converges to a value between 0.06 and 0.07 for the compound buoyancy and shear (KH+RT) driven flows. Vertical velocity fluctuation rms values at the mixing layer centerline are measured using a hot-wire technique. These rms values are correlated to the centerline mixing width growth rate, and this growth rate coefficient is found to lie between 0.06 and 0.07 at $\ensuremath{\tau}1$ for the KH+RT flows. The transition in flow dominance from shear instability to RTI is observed to correspond with Richardson numbers ($\mathrm{Ri}=\frac{\ensuremath{-}2hg\ensuremath{\Delta}\ensuremath{\rho}}{\ensuremath{\rho}\ensuremath{\Delta}{U}^{2}}$) of \ensuremath{-}1.5 to \ensuremath{-}2.5. Molecular mixing between the fluids is examined by looking at the probability density function distribution of the density fluctuations. A different type of mixing behavior is observed over time for the compound cases compared with the transient development of Rayleigh-Taylor driven mixing.