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The instability of the boundary layer over a disk rotating in an enforced axial flow
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10.1063/1.3662133
/content/aip/journal/pof2/23/11/10.1063/1.3662133
http://aip.metastore.ingenta.com/content/aip/journal/pof2/23/11/10.1063/1.3662133

Figures

Image of FIG. 1.
FIG. 1.

Basic-flow profiles for T s  = 0, 0.05, 0.15, and 0.25 (arrow indicates direction of increasing T s ).

Image of FIG. 2.
FIG. 2.

Neutral-stability curves in terms of predicted wavenumber for T s  = 0, 0.05, 0.15, and 0.25 (a)–(d). Solid line: numerical, dashed line: asymptotic.

Image of FIG. 3.
FIG. 3.

Neutral-stability curves in terms of predicted waveangle for T s  = 0, 0.05, 0.15, and 0.25 (a)–(d). Solid line: numerical, dashed line: asymptotic.

Image of FIG. 4.
FIG. 4.

Neutral-stability curves in the (α r , R L )-plane for T s  = 0 (dotted line), 0.05, 0.15, 0.25, 0.30, 0.35, and 0.40 (left to right).

Image of FIG. 5.
FIG. 5.

The effective mean velocity profiles (in the rotating frame) for T s  = 0.40 at Φ = 90°–0° in increments of 10° (bottom to top).

Image of FIG. 6.
FIG. 6.

Linear convective growth rates for stationary disturbances at various T s at a fixed extent of 215 in R L into the convectively unstable region.

Image of FIG. 7.
FIG. 7.

Re-scaled leading-order wavenumber against the re-scaled frequency shown for increasing axial flow T s .

Image of FIG. 8.
FIG. 8.

Re-scaled first-order waveangle against the re-scaled frequency shown for increasing axial flow T s .

Image of FIG. 9.
FIG. 9.

Neutral-stability curves calculated in the rotating frame for ω = 0 “–”; ω = 4 “– –”; ω = 7.9 “–.”; ω = 10 “···”; ω = −5 “–” (T s  = 0).

Image of FIG. 10.
FIG. 10.

Neutral-stability curves of traveling modes in the rotating frame for T s  = 0, 0.05, 0.15, and 0.25 (left to right).

Image of FIG. 11.
FIG. 11.

Growth rates for T s  = 0 in the rotating frame for various ω.

Image of FIG. 12.
FIG. 12.

Neutral-stability curves for T s  = 0.25 for traveling modes. Solid lines: numerical, dashed lines: asymptotic.

Image of FIG. 13.
FIG. 13.

Neutral-stability curves for traveling mode disturbances for T s  = 0; c = 0.8 “···”; c = 1 “–”; c = 5 “–.”; c = 20 “–x”.

Image of FIG. 14.
FIG. 14.

Neutral-stability curves for traveling mode disturbances for T s  = 0.05; c = 0.8 “···”; c = 1 “–”; c = 5 “–.”; c = 20 “–x”.

Image of FIG. 15.
FIG. 15.

Neutral-stability curves for traveling mode disturbances for T s  = 0.15; c = 0.8 “···”; c = 1 “–”; c = 5 “–.”; c = 20 “–x”.

Tables

Generic image for table
Table I.

Numerical values for the asymptotic expansions of and φ I in Eqs. (9) and (10), respectively.

Generic image for table
Table II.

Numerical values for the asymptotic expansions of and φ II in Eqs. (11) and (12), respectively.

Generic image for table
Table III.

First-order numerical values for the asymptotic expansions of and φ I in Eqs. (13) and (14), for x −2/3ω0 = −0.0001, −0.000862, 0.00017, and 0.000215 (left to right), which correspond to ω = −5, 4, 7.9, and 10, respectively, at R L  = 107.

Generic image for table
Table IV.

Leading-order numerical values for the asymptotic expansions of and φ II in Eqs. (17) and (18) for (left to right), which correspond to ω = −5,4, respectively, at R L  = 107 (the final column is the second branch for ).

Generic image for table
Table V.

Numerical values of quantities used in the asymptotic analysis.

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/content/aip/journal/pof2/23/11/10.1063/1.3662133
2011-11-30
2014-04-24
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: The instability of the boundary layer over a disk rotating in an enforced axial flow
http://aip.metastore.ingenta.com/content/aip/journal/pof2/23/11/10.1063/1.3662133
10.1063/1.3662133
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