Rayleigh–Taylor and shear driven mixing with an unstable thermal stratification

Abstract

A new water channel experiment has been used to study turbulent mixing driven by buoyancy, and by combined buoyancy and shear. Density differences were produced by thermal stratification. The experiment was statistically steady, and a space–time transformation in the streamwise direction permitted a continuous study of the mixing evolution. Dye and digitized photographs were used to study the mixing process. An ensemble average of images gave the average mixing layer growth rate and the distribution of light and heavy fluid in the mixing layer. The structure of the early growth of buoyancy dominated mixing and of combined shear and buoyancy mixing is presented. The mixing transition from combined shear and buoyancy mixing to buoyancy dominated mixing occurred at Richardson numbers from −5 to −11. It was found that buoyancy dominated a self-similar mixing stage for the range of flows (ΔU=0 to 2 cm/s) and density differences (Δρ=0.38 to 2.4 kg/m3). Transition to self-similar mixing occurred at a Reynolds number from 670 to 1200. The self-similar mixing width for all tests had a quadratic growth rate with an average acceleration constant of 0.070 and a standard deviation of 0.011.

Experimental characterization of initial conditions and spatio-temporal evolution of a small-Atwood-number Rayleigh–Taylor mixing layer

“…In the present experiments, the mean advection velocity is U m ≈ 4.75 cm/s, with the two stream velocities matched so that there is no shear due to mean velocity gradients. The sidewalls have been shown to have negligible influence on the growth rate of the mixing layer (Snider & Andrews 1994). Water channel measurements have also been shown to be statistically-stationary for higher-order moments of velocity and density fluctuations (Wilson 2002;Ramaprabhu 2003).…”

“…Another method for generating a Rayleigh-Taylor unstable interface (and the one used in this work) was pioneered by Snider and Andrews (1994), in which cold and hot water streams are initially separated by a thin splitter plate. After termination at the knife edge of the splitter plate, the resulting flow configuration is Rayleigh-Taylor unstable and a mixing layer develops downstream.…”

“…After termination at the knife edge of the splitter plate, the resulting flow configuration is Rayleigh-Taylor unstable and a mixing layer develops downstream. The water channel of Snider and Andrews (1994) was used in the current investigation, and is discussed in detail in § 3. Optical techniques were used to measure the self-similar quadratic-in-time growth of the mixing layer and the average volume fraction (non-dimensional density) profiles across the mixing layer.…”

“…The downstream distance from the trailing edge of the splitter plate x is converted to time t = x/U m using Taylor's hypothesis (Taylor 1938;Pope 2000). Time is normalized by the characteristic buoyancy timescale (Snider & Andrews 1994;Dalziel, Linden & Youngs 1999;Ramaprabhu & Andrews 2004a) ,…”

On the dynamics of magma mixing by reintrusion: implications for pluton assembly processes

“…Relevant works on mixing in enclosures as a result of initial conditions or boundary forcing include those of Danckwerts (1952), Bigg and Middleman (1974), McEwan (1983a,b), Ottino (1989), Duval (1992), Snider and Andrews (1994) and Linden et al (1994). These works are of particular interest to structural geologists as they pertain to the kinematic description of a time-varying¯ow ®eld.…”