1887
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Nonequilibrium energy spectrum in the subgrid-scale one-equation model in large-eddy simulation
Rent:
Rent this article for
USD
10.1063/1.4836795
/content/aip/journal/pof2/25/12/10.1063/1.4836795
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/12/10.1063/1.4836795

Figures

Image of FIG. 1.
FIG. 1.

Temporal variations in the average turbulent energy (⟨⟩, shown using the solid line (red)) and the dissipation rate (⟨ɛ⟩, the solid line with circles (blue)) obtained from DNS.

Image of FIG. 2.
FIG. 2.

Energy spectra normalized by (⟨⟨ɛ⟩⟩1/4ν5/4) obtained from the DNS data are shown. (a) ⟨ ()⟩ and are plotted versus ⟨⟨η⟩⟩ using the solid line with circles (red) and the solid line (blue), respectively, and |⟨ ()⟩| is plotted versus ⟨⟨η⟩⟩ using the black filled circles. The dotted lines indicate scaling with −5/3, −7/3, and −9/3. (b) is plotted versus ⟨⟨η⟩⟩ using the solid line (blue) and is plotted using the solid line with circles (red). The dotted lines indicate scaling with −7/3.

Image of FIG. 3.
FIG. 3.

Isocontours of deviatric spectra normalized by (⟨ɛ⟩1/4ν5/4) obtained from DNS are shown as functions of the wavenumber ⟨η⟩ and . Scaling is logarithmic, allowing for clearer display of the structure. The small frame shows the temporal variations of ⟨⟩ (solid line/red) and ⟨ɛ⟩ (solid line with circles/blue).

Image of FIG. 4.
FIG. 4.

Isocontours of the energy flux Π() normalized by ⟨ɛ⟩ obtained from DNS are shown as functions of the wavelength ⟨η⟩ and . Scaling is logarithmic. The small frame shows the temporal variations of ⟨⟩ (solid line/red) and ⟨ɛ⟩ (solid line with circles/blue).

Image of FIG. 5.
FIG. 5.

Distributions of the energy transfer function () normalized by ⟨⟨η⟩⟩⟨⟨ɛ⟩⟩ and flux Π() normalized by ⟨⟨ɛ⟩⟩ obtained from the DNS data are shown as functions of the wavelength ⟨⟨η⟩⟩. (a): Average of the deviation from the long term average in Phase 1; (b): Phase 2. The transfer function () is shown using the solid line (blue), and the flux Π() using the solid line with circles (red). The dotted lines show the distributions of () and Π() in Eq. (11) . Scaling is logarithmic.

Image of FIG. 6.
FIG. 6.

Temporal variations in the grid-scale and SGS quantities obtained from the filtered DNS data. The average grid-scale energy ⟨ ⟩ (shown using the black filled circles), SGS energy ⟨ ⟩ (solid line/blue), SGS dissipation term ⟨ɛ⟩ (dashed-dotted line/red), and the SGS dissipation approximated using the standard Smagorinsky model ⟨ɛ⟩ (open circles/red) are shown.

Image of FIG. 7.
FIG. 7.

Distributions of temporal cross correlation functions obtained using the filtered DNS data. The functions between the average grid-scale energy ⟨ ⟩ and the SGS energy ⟨ ⟩ ( (⟨ ⟩, ⟨ ⟩), shown using the solid line with circles (green), SGS production term ⟨⟩ ( (⟨ ⟩, ⟨⟩), solid line (red), and the SGS dissipation ⟨ɛ⟩ ( (⟨ ⟩, ⟨ɛ⟩), solid line with triangles (blue), are shown. The small inset shows the cross correlation functions averaged in Phase 1 (solid lines) and Phase 2 (dashed lines).

Image of FIG. 8.
FIG. 8.

Temporal variations in the average grid-scale energy ⟨ ⟩ and SGS energy ⟨ ⟩. Filtered DNS data (shown using the black filled circles) and the results obtained using the standard Smagorinsky model (dashed line/red), the one-equation model (solid line with circles/green), and the nonequilibrium Smagorinsky model (solid line/blue) are shown. Nonequilibrium denotes the nonequilibrium Smagorinsky model: (a) ⟨ ⟩; (b) ⟨ ⟩.

Image of FIG. 9.
FIG. 9.

Distributions of temporal cross correlation functions obtained using the one-equation model. The functions between the average grid-scale energy ⟨ ⟩ and the SGS energy ⟨ ⟩ ( (⟨ ⟩, ⟨ ⟩), shown using the solid line with circles (green)), SGS production term ⟨⟩ ( (⟨ ⟩, ⟨⟩), solid line (red)), and the SGS dissipation ⟨ɛ⟩ ( (⟨ ⟩, ⟨ɛ⟩), solid line with triangles (blue)), are shown. The small inset shows the cross correlation functions averaged in Phase 1 (solid lines) and Phase 2 (dashed lines).

Image of FIG. 10.
FIG. 10.

(a) Temporal variations in the average grid-scale energy ⟨ ⟩ (shown using the black line with open circles), SGS energy ⟨ ⟩ (solid line/blue), SGS dissipation term ⟨ɛ⟩ (filled circles/red), and the SGS production term ⟨⟩ (solid line with filled circles/green) obtained using the nonequilibrium Smagorinsky model are shown. (b) Distributions of temporal cross correlation functions obtained using the nonequilibrium Smagorinsky model. The functions between the average grid-scale energy ⟨ ⟩ and the SGS energy ⟨ ⟩ ( (⟨ ⟩, ⟨ ⟩), shown using the solid line with circles (green)), SGS production term ⟨⟩ ( (⟨ ⟩, ⟨⟩), solid line (red)), and the SGS dissipation ⟨ɛ⟩ ( (⟨ ⟩, ⟨ɛ⟩), solid line with triangles (blue)), are shown. The small inset shows the cross correlation functions averaged in Phase 1 (solid lines) and Phase 2 (dashed lines).

Image of FIG. 11.
FIG. 11.

Grid-scale portions of the energy spectra normalized by (⟨⟨ɛ⟩⟩1/4ν5/4) obtained using the standard and nonequilibrium Smagorinsky models are shown. ⟨ ()⟩, , and are plotted versus ⟨⟨η⟩⟩ using the solid line with circles, the solid line (blue), and the solid line with triangles (red), respectively. The dotted lines indicate scaling with −5/3, −7/3, and −9/3: (a) the standard Smagorinsky model; (b) the nonequilibrium Smagorinsky model.

Tables

Generic image for table
Table I.

Parameters for the computed case: Taylor microscale Reynolds number ; average kinetic energy ( = /2); average dissipation rate ɛ; integral length scale ; Taylor microscale λ; average Kolmogorov length η(=(ν3/ɛ)1/4); eddy turnover time according to , τ(=/ ); Kolmogorov time scale τ(=(ν/ɛ)1/2); characteristic time due to forcing ; eddy turnover time due to forcing (= / ); skewness of velocity fluctuation ; flatness of velocity fluctuation ; skewness of velocity derivative ( = ∂ /∂ ); flatness of velocity derivative . The second and third columns show the averages in Phase 1 and Phase 2, respectively (see Sec. III ).

Generic image for table
Table II.

Volume and temporal averaged values of the grid-scale energy and the SGS energy . DNS denotes the filtered DNS data, Smagorinsky denotes the standard Smagorinsky model, One-eq. denotes the one-equation model using the Adams-Bashforth method, and Nonequilibrium denotes the nonequilibrium Smagorinsky model.

Loading

Article metrics loading...

/content/aip/journal/pof2/25/12/10.1063/1.4836795
2013-12-10
2014-04-20
Loading

Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Nonequilibrium energy spectrum in the subgrid-scale one-equation model in large-eddy simulation
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/12/10.1063/1.4836795
10.1063/1.4836795
SEARCH_EXPAND_ITEM