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Simple models of turbulent flowsa)
a)This paper is based on the Otto Laporte Lecture delivered by the author on November 22, 2009, following the award of the APS Fluid Dynamics Prize at the American Physical Society Division of Fluid Dynamics Annual Meeting in Minneapolis.
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10.1063/1.3531744
/content/aip/journal/pof2/23/1/10.1063/1.3531744
http://aip.metastore.ingenta.com/content/aip/journal/pof2/23/1/10.1063/1.3531744

Figures

Image of FIG. 1.
FIG. 1.

Sketch of Warhaft’s experiment on a line source in grid turbulence showing the -coordinate system with origin at the middle of the heated wire (which is the line source of temperature) and the (Gaussian) mean excess temperature profile of width .

Image of FIG. 2.
FIG. 2.

Width of the thermal wake (normalized by at the source) against distance from the source normalized by the distance of the source from the grid: symbols, experimental data (Refs. 11 and 12); line, from the model.

Image of FIG. 3.
FIG. 3.

Samples of fluid-particle paths for short times (, top) and for long times (, bottom) obtained from the Langevin model. The dashed lines show , the standard deviation of . Normalization is by the Lagrangian integral time scale and the rms velocity .

Image of FIG. 4.
FIG. 4.

Width of the thermal wake (normalized by at the source) against distance from the source normalized by the distance of the source from the grid: symbols, experimental data (Refs. 11 and 12); dashed line, from the Langevin model for fluid particles; solid line, from the Langevin model for Brownian particles.

Image of FIG. 5.
FIG. 5.

Axial profile of the ratio of the rms temperature fluctuation to the mean temperature excess on the centerline downstream of the line source: symbols, experimental data (Ref. 11); line, calculations using the IECM model (Ref. 6).

Image of FIG. 6.
FIG. 6.

Radial profiles of the rms temperature fluctuation normalized by its centerline value at axial locations (from top to bottom) : symbols, experimental data (Ref. 11); line, calculations using the IECM model (Ref. 6).

Image of FIG. 7.
FIG. 7.

Axial profiles on the centerline of the correlation coefficient between the scalars from a pair of line sources: symbols, experimental data (Ref. 11); lines, calculations using the IECM model (Ref. 6). The separation between the sources is (from top to bottom downstream) .

Image of FIG. 8.
FIG. 8.

Sketch of a highly simplified, plane, lifted flame formed from a cold fuel jet issuing into hot quiescent air. Also shown are the domain and the mesh used in the particle/mesh method.

Image of FIG. 9.
FIG. 9.

Scatter plots of particles in the solution domain for the lifted jet flame. The particles are grayscale-coded (color-coded online) by mixture fraction (left) and by product mass fraction (right) (enhanced online). [URL: http://dx.doi.org/10.1063/1.3531744.1]10.1063/1.3531744.1

Image of FIG. 10.
FIG. 10.

Cell means of product mass fraction obtained from the particle/mesh method applied to the simple lifted flame. Left: contour plot of instantaneous cell means. Right: lateral profile at of the instantaneous [circles (red)] and time-averaged [squares (blue)] cell mean (enhanced online). [URL: http://dx.doi.org/10.1063/1.3531744.2]10.1063/1.3531744.2

Image of FIG. 11.
FIG. 11.

Lift-off height (normalized by the jet diameter ) against coflow temperature : symbols, experimental data (Ref. 39); line with symbols, PDF calculations (Ref. 41).

Image of FIG. 12.
FIG. 12.

The composition space (projected onto the mixture fraction/temperature plane) for the Cabra lifted flame, showing compositions corresponding to pure fuel, pure coflow, inert mixing, and chemical equilibrium.

Image of FIG. 13.
FIG. 13.

Scatter plot of mixture fraction and temperature of particles emanating from the fuel jet in PDF calculations (Ref. 42) of the Cabra flame. Print version, particles at ; on-line version, animation with time corresponding to (enhanced online). [URL: http://dx.doi.org/10.1063/1.3531744.3]10.1063/1.3531744.3

Image of FIG. 14.
FIG. 14.

Compensated second-order Lagrangian structure functions: solid lines, DNS (Ref. 70) at Reynolds numbers (from bottom to top) , 86, 140, 235, 393, 595, 1000; dashed line, Langevin model with .

Image of FIG. 15.
FIG. 15.

The Langevin-model constant against Reynolds number: symbols, from DNS (Ref. 70) and Eq. (67); line, empirical fit, Eq. (68).

Image of FIG. 16.
FIG. 16.

Compensated second-order Lagrangian structure functions: solid lines, DNS (Ref. 70) at Reynolds numbers (from bottom to top) , 86, 140, 235, 393, 595, 1000; dashed lines, Langevin model with obtained from Eq. (67).

Image of FIG. 17.
FIG. 17.

Compensated second-order Lagrangian structure functions: solid lines, DNS (Ref. 70) at Reynolds numbers (from bottom to top) , 86, 140, 235, 393, 595, 1000; dashed lines, from Sawford’s model (Ref. 7), Eq. (69).

Image of FIG. 18.
FIG. 18.

Standardized PDFs of acceleration from DNS (Ref. 73): outer solid line (red), unconditional PDF; inner solid lines (six indistinguishable lines), PDFs conditional on pseudodissipation quintiles (magenta, online), and the cubic Gaussian equation [Eq. (73)] (green, online); inner dashed line, Gaussian (blue).

Image of FIG. 19.
FIG. 19.

Kurtosis of , the logarithm of pseudodissipation, obtained from DNS (Ref. 73) against Reynolds number compared to the Gaussian value of 3.

Image of FIG. 20.
FIG. 20.

Autocorrelation function of , the logarithm of pseudodissipation, obtained from DNS (Ref. 77) compared to the exponential (dashed line).

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2011-01-18
2014-04-16
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Simple models of turbulent flowsa)
http://aip.metastore.ingenta.com/content/aip/journal/pof2/23/1/10.1063/1.3531744
10.1063/1.3531744
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