Density ratio dependence of Rayleigh–Taylor mixing for sustained and impulsive acceleration histories

Abstract

The turbulent Rayleigh–Taylor instability is investigated over a comprehensive range of fluid density ratio (R)1.3⩽R⩽50 [0.15⩽A=(R−1)/(R+1)⩽0.96] and different acceleration histories g(t) using the Linear Electric Motor. The mixing layer is diagnosed with backlit photography and laser-induced fluorescence. For a constant acceleration, the bubble (2) and spike (1) amplitudes are found to increase as hi=αiAgt2 with α2∼0.05±0.005 and α1∼α2RDα with Dα∼0.33±0.05. For temporally varying accelerations Ag(t)>0, this can be generalized to hi=2αiAS using S=[∫gdt]2/2 rather than the displacement Z=∫∫gdt′ dt. For impulsive accelerations, S remains constant during the coast phase and the amplitudes obey a power law hi∼tθi with θ2∼0.25±0.05 and θ1∼θ2RDθ with Dθ∼0.21±0.05. These values of Dα and Dθ compare favorably with numerical simulations and mix models. The average diameter at the mixing front for bubbles is found to increase as d2∼h2(1+A)/4 in qualitative agreement with “merger” models, but the associated dhi/dt is two times larger than the terminal velocity of an isolated bubble. The spikes become relatively narrow at large R, yet they still grow as gt2.

Computing multi-mode shock-induced compressible turbulent mixing at late times

“…Furthermore, with reference to Equation (2.3), the values of the growth exponent computed by the non-linear regression (NLR) analysis are summarised and compared against published results in Table 2. The growth exponent in the compressible simulation is found to be in good agreement with both the experiments of Dimonte and Schneider (2000) and the numerical simulations of Thornber et al (2010). Excellent agreement is also found with Youngs (2004), where θ = 0.243 was obtained from a long-time compressible simulation; the difference between Youngs (2004) and our simulations is approximately 0.001.…”

“…Experiments (Dimonte and Schneider 2000) confirmed the results giving an exponent for the formula (2.7) of 0.21 ± 0.05. Studying separately the evolution of bubble and spikes, the authors found that θ b is substantially independent from the Atwood number and has a value of 0.25 ± 0.05, whereas the spikes exponent has a very similar value to θ b only for A t < 0.8.…”

“…When the interface is characterised by a constant power spectrum of a combination of narrowband wavenumbers, a θ ≈ 0.23 was computed, which is in agreement with Dimonte and Schneider (2000). On the other hand, the value of θ ≈ 0.62 was found in the case that the interface is formed by a broadband of modes with a power spectrum proportional to k −2 , which is close to the upper bound limit calculated by the theoretical analysis presented in §2.1.…”

Analytic approach to nonlinear hydrodynamic instabilities driven by time-dependent accelerations

“…More recently, experiments have been performed [5,6] with several deliberately chosen time-dependent s t g ) ' ( . These experimental profiles for ) (t g will form our starting point.…”

Concept Development for Astrophysically Relevant Turbulence on NIF

“…The three dimensional model predictions were compared to the Linear Electric Motor (LEM) experimental results presented by Dimonte & Schneider [4], with good agreement for the scaling parameters α b,s and h b / λ . However, the experiments did not provide a direct measurement of the bubble front size distribution due to their 3D nature, and the models validity in this manner was not confirmed.…”