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Statistical measurements of scaling and anisotropy of turbulent flows induced by Rayleigh-Taylor instability
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10.1063/1.4774338
/content/aip/journal/pof2/25/1/10.1063/1.4774338
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/1/10.1063/1.4774338

Figures

Image of FIG. 1.
FIG. 1.

Visualization of a vertical slice of the density field in the RTI mixing layer at late time for the = 0.5 case. Heavy fluid is dark, light fluid is light. Gravity is directed downwards.

Image of FIG. 2.
FIG. 2.

(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 /3 in the middle of the mixing layer. (The gap in the = 0.2 data resulted from data lost in a catastrophic file system failure.) (b) The growth of the product width is shown for the different Atwood numbers.

Image of FIG. 3.
FIG. 3.

Vertical profiles (horizontal averages) of fluctuation intensity for (a) velocity components and (b) velocity derivative components are shown at time = 25 in the = 0.5 case, demonstrating statistical equivalences and the degree of anisotropy.

Image of FIG. 4.
FIG. 4.

Vertical profiles (horizontal averages) of the fluctuation intensity of velocity derivative functions at time = 25 in the = 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 .

Image of FIG. 5.
FIG. 5.

The correlation functions of velocity components and density for the = 0.5 case at = 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 | ) in (a) is plotted with the separation length scaled by 1/√2. Statistically equivalent terms have been averaged together.

Image of FIG. 6.
FIG. 6.

Midplane 2nd-order structure function for the vertical velocity, scaled by ⟨ ⟩, in the = 0.5 case at = 25 for (a) transverse separations ( = δ) and (b) longitudinal separations ( = ±δ) showing behavior for small separations and approximate behavior for large separations. The model in (21) is shown with dashed lines using an eyeball fit for parameter .

Image of FIG. 7.
FIG. 7.

One-dimensional spectra of (a) velocity and (b) vorticity at midplane at = 25 in the = 0.5 case. Vertical spectra (in ) for velocity components were constructed using Fourier transforms of vertical autocorrelation functions. Statistically equivalent terms have been averaged together.

Image of FIG. 8.
FIG. 8.

Compensated 2D horizontal spectra for the vertical velocity component () (thick lines) and for the sum of all velocity components () (thin lines) calculated near the midplane at = 25 for the = 0.5 case. In (a) the Kolmogorov scaling is used, and in (b) the Rayleigh-Taylor scaling proposed by Zhou is used.

Image of FIG. 9.
FIG. 9.

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.

Image of FIG. 10.
FIG. 10.

Vertical profiles of (a) skewness and (b) flatness for velocity derivatives at = 25 for the = 0.5 case.

Image of FIG. 11.
FIG. 11.

Histograms of the cosine of angles between strain rate eigenvectors, vorticity, and density gradient in the middle of the mixing layer at = 25 in the = 0.5 case. Values near unity correspond to parallel alignment of the vectors, and values near zero correspond to orthogonal alignment.

Tables

Generic image for table
Table I.

Velocity and velocity-derivative isotropy in homogeneous isotropic turbulence (theoretical) and late-time ( = 25) Rayleigh-Taylor instability flow with gravity in direction 3.

Generic image for table
Table II.

Turbulence statistics for the = 0.5 case at = 25 for different spatial averaging domains.

Generic image for table
Table III.

Late-time turbulence statistics for different Atwood numbers with “mid-slab” average.

Generic image for table
Table IV.

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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/content/aip/journal/pof2/25/1/10.1063/1.4774338
2013-01-17
2014-04-21
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Statistical measurements of scaling and anisotropy of turbulent flows induced by Rayleigh-Taylor instability
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/1/10.1063/1.4774338
10.1063/1.4774338
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