Experimental study of the single-mode three-dimensional Rayleigh-Taylor instability

Abstract

The three-dimensional Rayleigh-Taylor instability is studied in a low Atwood number (A≈0.15) miscible fluid system. The two fluids are contained within a Plexiglas tank that is mounted on vertical rails and accelerated downward by a weight and pulley system. A net acceleration between 13 and 23m∕s2 can be maintained, resulting in an effective body force equivalent to 0.33–1.35 times Earth’s gravity. A single-mode, three-dimensional perturbation is produced by oscillating the tank, which has a square cross section, along its diagonal. Early time measured growth rates are shown to have good agreement with linear stability theory. At late time, the instability exhibits a nonconstant vertical interfacial velocity in agreement with the recent numerical computations of Ramaprabhu et al. [Phys. Rev. E 74, 066308 (2006)]. Both the late-time bubble and spike velocities have values greater than those predicted by both the simple buoyancy-drag model developed by Oron et al. [Phys. Plasmas 8, 2883 (2001)] and the potential flow model of Goncharov [Phys. Rev. Lett. 88, 134502 (2002)]. The disagreement with the models can be attributed to the formation of vortices, in this case vortex rings, observed in the experiments but not accounted for by the models.

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

“…Popil & Curzon 1979), and; planar or spherical laser-driven experiments that include surface perturbations at material interfaces (Kilkenny et al 1994;Lindl 1998;Oron et al 1999;Subramanian, Zebib & McQuillan 2005). It is difficult to quantify the initial perturbations in experiments that impose perturbations in two dimensions; however, several such experiments have yielded measurements for the single-mode instability evolution (Jacobs & Catton 1988;Wilkinson 2004). Additional modeling issues involving the specification of initial conditions are briefly discussed below.…”

“…They obtained an approximate single-mode perturbation at the density interface by oscillating a paddle, and measured the growth of individual bubbles and spikes using high-speed photography. Other researchers have also used some type of accelerated tank containing miscible or immiscible fluids of different densities to investigate the growth of Rayleigh-Taylor instability-driven mixing layers (Ratafia 1973;Cole & Tankin 1973;Popil & Curzon 1979;Read 1984;Jacobs & Catton 1988;Kucherenko et al 1994Kucherenko et al , 1997Kucherenko et al , 2003aDimonte & Schneider 1996, Dimonte 1999Wilkinson 2004).…”

“…Some experiments imposed an approximate sinusoidal perturbation at the two-fluid interface and primarily used ordinary photographic techniques to measure the growth of individual bubbles and spikes (Ratafia 1973;Cole & Tankin 1973;Popil & Curzon 1979;Jacobs & Catton 1988;Wilkinson 2004). In addition to the measurement of the mixing layer width, Wilkinson (2004) used planar laser-induced fluorescence (PLIF) to measure the growth and internal structure of the single-mode, three-dimensional Rayleigh-Taylor instability.…”

“…In addition to the measurement of the mixing layer width, Wilkinson (2004) used planar laser-induced fluorescence (PLIF) to measure the growth and internal structure of the single-mode, three-dimensional Rayleigh-Taylor instability. Other researchers have either allowed ambient noise or intentionally-created initial, multi-mode perturbations to seed the instability (Read 1984;Dimonte & Schneider 1996;Dimonte 1999;Kucherenko et al 1997Kucherenko et al , 2003a.…”

Evolution of the single-mode Rayleigh-Taylor instability under the influence of time-dependent accelerations

“…While the RT-dominated flow in these examples is turbulent and highly nonlinear, a detailed understanding of such flows must be built from a description of the corresponding elemental, single-scale problem [12][13][14][15][16][17][18][19][20]. For an initially sinusoidal, interfacial perturbation characterized by a perturbation amplitude (h 0 ) and wavenumber k (≡ 2π/λ), linear theory [1][2]21 predicts exponential growth according to:…”