Visualization of a vertical slice of the density field in the RTI mixing layer at late time for the A = 0.5 case. 5 Heavy fluid is dark, light fluid is light. Gravity is directed downwards.
(a) Isotropy of the vorticity field is shown as a function of time, measured by the ratio of vertical to horizontal enstrophy components averaged over a vertical extent of h/3 in the middle of the mixing layer. (The gap in the A = 0.2 data resulted from data lost in a catastrophic file system failure.) (b) The growth of the product width h is shown for the different Atwood numbers.
Vertical profiles (horizontal averages) of fluctuation intensity for (a) velocity components and (b) velocity derivative components are shown at time t = 25 in the A = 0.5 case, demonstrating statistical equivalences and the degree of anisotropy.
Vertical profiles (horizontal averages) of the fluctuation intensity of velocity derivative functions at time t = 25 in the A = 0.5 case: (a) vorticity components, (b) cross terms, (c) dissipation components, and (d) dissipation terms. The vertical position is scaled by the product width of the mixing layer h.
The correlation functions of velocity components and density for the A = 0.5 case at t = 25 using mid-slab averaging for horizontal correlations in (a) and (b), midplane averaging for vertical correlations in (a) and (c), and global vertical correlations in (d). The longitudinal horizontal correlation C uu (δx|z 0) in (a) is plotted with the separation length scaled by 1/√2. Statistically equivalent terms have been averaged together.
Midplane 2nd-order structure function for the vertical velocity, scaled by ⟨w 2⟩, in the A = 0.5 case at t = 25 for (a) transverse separations (r = δx) and (b) longitudinal separations (r = ±δz) showing r 2 behavior for small separations and approximate r 2/3 behavior for large separations. The model in (21) is shown with dashed lines using an eyeball fit for parameter B.
One-dimensional spectra of (a) velocity and (b) vorticity at midplane at t = 25 in the A = 0.5 case. Vertical spectra (in k 3) for velocity components were constructed using Fourier transforms of vertical autocorrelation functions. Statistically equivalent terms have been averaged together.
Compensated 2D horizontal spectra for the vertical velocity component E 33(k) (thick lines) and for the sum of all velocity components E ii (k) (thin lines) calculated near the midplane at t = 25 for the A = 0.5 case. In (a) the k −5/3 Kolmogorov scaling is used, and in (b) the k −7/4 Rayleigh-Taylor scaling proposed by Zhou 21 is used.
Horizontal midplane spectra for (a) vertical and (b) horizontal kinetic energy rate terms: buoyancy production (dashed line), pressure-strain (thin solid line), and dissipation (medium solid line). The pressure-strain term is a sink (–) for the vertical kinetic energy and a source (+) for the horizontal kinetic energy. The thick curves show the corresponding vertical and horizontal velocity spectra.
Vertical profiles of (a) skewness and (b) flatness for velocity derivatives at t = 25 for the A = 0.5 case.
Histograms of the cosine of angles between strain rate eigenvectors, vorticity, and density gradient in the middle of the mixing layer at t = 25 in the A = 0.5 case. Values near unity correspond to parallel alignment of the vectors, and values near zero correspond to orthogonal alignment.
Velocity and velocity-derivative isotropy in homogeneous isotropic turbulence (theoretical) and late-time (t = 25) Rayleigh-Taylor instability flow with gravity in direction 3.
Turbulence statistics for the A = 0.5 case at t = 25 for different spatial averaging domains.
Late-time turbulence statistics for different Atwood numbers with “mid-slab” average.
Mean properties of strain rate eigenvalues, vorticity, and density gradient in the middle of the mixing layer at late time in the simulations for different Atwood numbers.
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