Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-13T01:36:23.241Z Has data issue: false hasContentIssue false
  • English
  • Français

The boundary layer induced by a convected two-dimensional vortex

Published online by Cambridge University Press:  20 April 2006

T. L. Doligalski  and
J. D. A. Walker
T. L. Doligalski
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, Indiana
J. D. A. Walker
Affiliation:
Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, Pennsylvania
Get access Rights & Permissions [Opens in a new window]

Abstract

The response of a wall boundary layer to the motion of a convected vortex is investigated. The principal cases considered are for a rectilinear filament of strength –κ located a distance a above a plane wall and convected to the right in a uniform flow of speed U∞*. The inviscid solution predicts that such a vortex will remain at constant height a above the wall and be convected with constant speed αU∞*. Here α is termed the fractional convection rate of the vortex, and cases in the parameter range 0 [les ] α < 1 are considered. The motion is initiated at time t* = 0 and numerical calculations of the developing boundary-layer flow are carried out for α = 0, 0.2, 0.4, 0.55, 0.7, 0.75 and 0.8. For α < 0.75, a rapid lift-up of the boundary-layer streamlines and strong boundary-layer growth occurs in the region behind the vortex; in addition an unusual separation phenomenon is observed for α [les ] 0.55. For α [ges ] 0.75, the boundary-layer development is more gradual, but ultimately substantial localized boundary-layer growth also occurs. In all cases, it is argued that a strong inviscid–viscous interaction will take place in the form of an eruption of the boundary-layer flow. The generalization of these results to two-dimensional vortices with cores of finite dimension is discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 139 , February 1984 , pp. 1 - 28
Copyright
© 1984 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Belcher, R. J., Burggraf, O. R., Cooke, J. C., Robins, A. J. & Stewartson, K. 1971 Limit-less boundary layers. In Recent Research on Unsteady Boundary Layers, pp. 1444–1446. Laval University Press. Quebec, Canada.
Blasius, H. 1908 Grenzschichten in Flüssigkeiten mit kleiner Reibung Z. Math. Phys. 56, 1–37.Google Scholar
Cebeci, T. 1979 The laminar boundary layer on a circular cylinder started impulsively from rest J. Comp. Phys. 31, 153–172.Google Scholar
Clements, R. R. & Maull, D. J. 1975. The representation of sheets of vorticity by discrete vortices. Prog. Aero. Sci. 16, 129–129.
Collins, W. M. & Dennis, S. C. R. 1973 Flow past an impulsively started circular cylinder J. Fluid Mech. 60, 105–127.Google Scholar
Dennis, S. C. R. & Walker, J. D. A. 1971 The initial flow past an impulsively started sphere at high Reynolds numbers J. Engng Maths 5, 263–278.Google Scholar
Dennis, S. C. R. & Walker, J. D. A. 1972 Numerical solutions for time-dependent impulsively started sphere Phys. Fluids 15, 517–525.Google Scholar
Doligalski, T. L. 1980 The influence of vortex motion on wall boundary layers. Ph.D. dissertation, Lehigh University.
Doligalski, T. L., Smith, C. R. & Walker, J. D. A. 1980 A production mechanism for turbulent boundary layers. In Viscous Drag Reduction (ed. G. Hough); Prog. Astro. Aero. 72, 47–72.
Elliot, J. W., Cowley, S. J. & Smith, F. T. 1983 Breakdown of boundary layers. Geophys. Astrophys. Fluid Dyn. (to appear).Google Scholar
Ece, M. C., Walker, J. D. A. & Doligalski, T. L. 1983 The boundary layer on an impulsively started rotating and translating cylinder. Phys. Fluids. (to appear).Google Scholar
Falco, R. E. 1977 Coherent motions in the outer region of turbulent boundary layers. Phys. Fluids Suppl. 20, S124–S132.Google Scholar
Falco, R. E. 1978 The role of outer flow coherent motions in the production of turbulence near a wall. In Proc. AFOSR Workshop on Coherent Structure of Turbulent Boundary Layers (ed. C. Smith & D. Abbott). Lehigh University.
Falco, R. E. 1982 A synthesis and model of turbulence structure in the wall region. In Structure of Turbulence in Heat and Mass Transfer (ed. Z. P. Zaric). Hemisphere.
Fendell, F. E. 1972 Singular perturbation and turbulent shear flow near walls J. Astro. Sci. 20, 129–165.Google Scholar
Harvey, J. K. 1958 Some measurements on a yawed slender delta wing with leading edge separation. British Aero. Res. Counc. R & M 3160.Google Scholar
Harvey, J. K. & Perry, F. J. 1971 Flowfield produced by trailing vortices in the vicinity of the ground AIAA J. 9, 1659–1660.Google Scholar
Head, M. R. & Bandyopadhyay, P. 1981 New aspects of turbulent boundary-layer structure J. Fluid Mech. 107, 297–338.Google Scholar
Hiemenz, K. 1911 Die Grenzschicht an einem in den gleichförmigen Flüssigkeitstrom eingetauchten geraden Kreiszylinder. Dinglers J. 326, 321–321, 344–344, 357–357, 391–391, 409–409.Google Scholar
Maccormack, R. W. 1969 The effect of viscosity in hypervelocity impact cratering. AIAA Paper 69–354, Cincinnati, Ohio.Google Scholar
Milne-Thompson, L. M. 1960 Theoretical Hydrodynamics, 4th edn. Macmillan.
Nychas, S. G., Hershey, H. C. & Brodkey, R. S. 1973 A visual study of turbulent shear flow J. Fluid Mech. 61, 513–540.Google Scholar
Ornberg, T. 1964 A note on the flow around delta wings. Royal Inst. of Tech., Sweden, KTH-Aero TN 38.Google Scholar
Rayleigh, Lord 1911 On the motion of solid bodies through viscous liquids Phil. Mag. 21, 697–711.Google Scholar
Riley, N. 1975 Unsteady laminar boundary layers SIAM Rev. 17, 274–297.Google Scholar
Sears, W. R. & Telionis, D. P. 1975 Boundary-layer separation in unsteady flow SIAM J. Appl. Maths 28, 215–235.Google Scholar
Shanks, D. 1955 Nonlinear transformations of divergent and slowly convergent sequences J. Math. Phys. 34, 1–42.Google Scholar
Van Dommelen, L. L. 1981 Unsteady boundary layer separation. Ph.D. thesis, Cornell University.
Van Dommelen, L. L. & Shen, S. F. 1980 The spontaneous generation of the singularity in a separating laminar boundary layer J. Comp. Phys. 38, 125–140.Google Scholar
Van Dyke, M. 1975 Perturbation Methods in Fluid Mechanics. Parabolic.
Walker, J. D. A. 1978 The boundary layer due to rectilinear vortex. Proc. R. Soc. Lond A 359, 167–188.Google Scholar
Willmarth, W. W. 1975 Structure of turbulence in boundary layers Adv. Appl. Mech. 15, 159–254.Google Scholar
Williams, J. C. 1977 Unsteady boundary layers Ann. Rev. Fluid. Mech. 9, 113–144.Google Scholar