Local wave-number model for inhomogeneous two-fluid mixing.

We analyze the local wave-number (LWN) model, a two-point spectral closure model for turbulence, as applied to the Rayleigh-Taylor (RT) instability, the flow induced by the relaxation of a statically-unstable density stratification. Model outcomes are validated against data from 3D simulations of the RT instability. In the first part of the study we consider the minimal model terms required to capture inhomogeneous mixing and show that this version, with suitable model coefficients, is sufficient to capture the evolution of important mean global quantities including mix-width, turbulent mass flux velocity, and Reynolds stress, if the start time is chosen such that the earliest transitions are avoided. However, this simple model does not permit the expected finite asymptote of the density-specific-volume covariance b. In the second part of the study, we investigate two forms for a source term for the evolution of the spectrum of density-specific-volume covariance for the LWN model. The first includes an empirically motivated calibration of the source to achieve the final asymptotic state of constant b. The second form does not require calibration but, in conjunction with enhanced diffusion and drag captures the full evolution of all the dynamical quantities, namely, the mix-layer growth, turbulent mass-flux velocity, Reynolds stress, as well as the desired behavior of b.

Rayleigh-Taylor instability with complex acceleration history.

Experiments and numerical simulations are performed on the Rayleigh-Taylor instability with a complex acceleration history g(t) consisting of consecutive periods of acceleration, deceleration, and acceleration. The dominant bubbles and spikes that grow in the initial unstable phase are found to be shredded by the trailing structures during the stable deceleration phase. This reduces their diameter at the front and increases the atomic mixing such that the growth during the final unstable acceleration is retarded. The simulations are able to describe the bubble evolution only if broadband initial perturbations are assumed. Such a complex g(t) is useful for validating mix models.