A numerical study of the influence of initial perturbations on the turbulent Rayleigh–Taylor instability

Abstract

The effect of initial conditions on the growth rate of turbulent Rayleigh-Taylor (RT) mixing has been studied using carefully formulated numerical simulations. A monotone integrated large-eddy simulation (MILES) using a finite-volume technique was employed to solve the three-dimensional incompressible Euler equations with numerical dissipation. The initial conditions were chosen to test the dependence of the RT growth coefficient (α b ) and the self-similar parameter (β b = λ b /h b ) on (i) the amplitude, (ii) the spectral shape, (iii) the longest wavelength imposed, and (iv) mode-coupling effects. With long wavelengths present in the initial conditions, α b was found to increase logarithmically with the initial amplitudes, while β b is less sensitive to amplitude variations. The simulations are in reasonable agreement with the predictions for α b from a recently proposed model, but not for β b . In the opposite limit where mode-coupling dominates, no such dependence on initial amplitudes is observed, and α b takes a universal lower-bound value of ∼ 0.03 ± 0.003. This may explain the low values of α b reported by most numerical simulations that are initialized with annular spectra of short-wavelength modes and hence evolve purely through mode-coupling. Small-scale effects such as molecular mixing and kinetic energy dissipation showed a weak dependence on the structure of initial conditions. Initial density spectra with amplitudes distributed as k 0 , k −1 and k −2 were used to investigate the role of the spectral slopes on the development of turbulent RT mixing. Furthermore, in a separate study, the longest wavelength imposed in the initial wavepacket was also varied to determine its effect on α b . It was found that the slopes of the initial spectra, and the longest wavelength imposed had little effect on the RT growth parameters.

Numerical investigation of initial condition effects on Rayleigh-Taylor instability with acceleration reversals

“…The influence of ICs on classical RT-unstable flows has received considerable attention in the literature [12,19,[38][39][40][41]. Previous studies [17,42] have identified two alternative phenomenological models that describe the convergence towards self-similarity (Eq.…”

“…2) in the classical case of RTI with a broad-band multimode initial perturbation undergoing constant acceleration. The first such approach, known as bubble merger, considers that two or more bubbles may merge and form larger structures as a part of a continuous and repetitive process during the evolution of the mixing layer [17,19]. In contrast, bubble competition involves amplification and saturation of long wavelengths and they lead the flow.…”

“…Haan [43] postulated that the transition to nonlinearity is triggered when the sum of modal amplitudes reaches ~σ/k, implying that individual modes may become non-linear well before their amplitudes reach the non-linear threshold (σ) due to the interaction of adjacent modes. Several studies on constant acceleration RTI [12,18,19,44] have shown that it is possible to control the time elapsed before structures in the flow develop full non-linearity, by modifying the initial amplitudes of modes so some saturate more quickly than others. Mean growth rates of the mixing layer become correspondingly modified.…”

“…Mean growth rates of the mixing layer become correspondingly modified. Several of these studies employed the RTI-3D code [12,19,23,45] and demonstrated that ICs with longer wavelengths lead to a faster growth of the mixing layer indicated that the asymptotic growth rate (which can be calculated using Eq.9) may not be universal. Moreover, they argue that because the flow depends throughout its lifespan on ICs, the flow cannot ever be regarded as truly self-similar.…”

“…However, there a universal value for the growth parameters α b and α s is not known and systematic discrepancies in measured values between experimental and numerical studies are attributed to the choice or selection of ICs, [12,[17][18][19]. Computational studies on RTI with constant acceleration by Ramabraphu et al [19] and Banerjee and Andrews [12] have investigated the effect of spectral bandwidth, spectral shape, and discrete banded spectra; for verification and comparison, we have chosen our ICs to match closely those used in these earlier studies.…”