DOI: 10.1017/s0022112075000535. On rotationally symmetric flow above an infinite rotating disk

On rotationally symmetric flow above an infinite rotating disk

10.1017/s0022112075000535

Crossref journal-article

Cambridge University Press (CUP)

Journal of Fluid Mechanics (56)

Abstract

The similarity equations for rotationally symmetric flow above an infinite counter–rotating disk are investigated both numerically and analytically. Numerical solutions are found when α, the ratio of the disk's angular speed to that of the rigidly rotating fluid far from it, is greater than −0.68795. It is deduced that there exists a critical value αcr, of α above which finite solutions are possible. The value of α and the limiting structure as α → αcrare found using the method of matched asymptotic expansions. The flow structure is found to consist of a thin viscous wall region above which lies a thick inviscid layer and yet another viscous transition layer. Furthermore, this structure is not unique: there can be any number of thick inviscid layers, each separated from the next by a viscous transition layer, before the outer boundary conditions on the solution are satisfied. However, comparison with the numerical solutions indicates that a single inviscid layer is preferred.

Bibliography

Bodonyi, R. J. (1975). On rotationally symmetric flow above an infinite rotating disk. Journal of Fluid Mechanics, 67(4), 657â666.

Authors 1

R. J. Bodonyi (first)

References 9 Referenced 22

Batchelor, G. K. 1951 Note on a class of solutions of the Navier-Stokes equations representing steady rotationally-symmetric flow.Quart. J. Mech. Appl. Math.,4,29. (10.1093/qjmam/4.1.29)
Ockendon, H. 1972 An asymptotic solution for the steady flow above an infinite rotating disc with suction.Quart. J. Mech. Appl. Math.,25,291. (10.1093/qjmam/25.3.291)
Bodonyi, R. J. 1973 The laminar boundary layer on a finite rotating disc. Ph.D. dissertation,The Ohio State University.
Mcleod, J. B. 1970 A note on rotationally symmetric flow above an infinite rotating disc.Mathematika,17,243. (10.1112/S0025579300002916)
Rogers, M. H. & Lance, G. N. 1960 The rotationally symmetric flow of a viscous fluid in the presence of an infinite rotating disk.J. Fluid Mech.,7,617. (10.1017/S0022112060000335)
Kármán, T. Von 1921 Über laminare und turbulente Reibung.2. angew. Math. Mech.,1,233. (10.1002/zamm.19210010401)
Kuiken, H. K. 1971 The effect of normal blowing on the flow near a rotating disk of infinite extent.J. Fluid Mech.,47,789. (10.1017/S002211207100137X)
Bödewadt, V. T. 1940 Die Drehstromung uber festem Grunde.2. angew. Math. Mech.,20,241.
Evans, D. J. 1969 The rotationally symmetric flow of a viscous fluid in the presence of an infinite rotating disc with uniform suction.Quart. J. Mech. Appl. Math.,22,467. (10.1093/qjmam/22.4.467)

Dates

Type	When
Created	19 years, 5 months ago (March 29, 2006, 3:51 a.m.)
Deposited	6 years, 4 months ago (April 17, 2019, 9:45 a.m.)
Indexed	4 weeks ago (Aug. 7, 2025, 4:47 p.m.)
Issued	50 years, 6 months ago (Feb. 25, 1975)
Published	50 years, 6 months ago (Feb. 25, 1975)
Published Online	19 years, 5 months ago (March 29, 2006)
Published Print	50 years, 6 months ago (Feb. 25, 1975)

Funders 0

None

BibTeX

@article{Bodonyi_1975, title={On rotationally symmetric flow above an infinite rotating disk}, volume={67}, ISSN={1469-7645}, url={http://dx.doi.org/10.1017/s0022112075000535}, DOI={10.1017/s0022112075000535}, number={4}, journal={Journal of Fluid Mechanics}, publisher={Cambridge University Press (CUP)}, author={Bodonyi, R. J.}, year={1975}, month=feb, pages={657–666} }

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