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Modulated stagnation-point flow and steady streaming

Published online by Cambridge University Press:  21 April 2006

Gregory J. Merchant  and
Stephen H. Davis
Gregory J. Merchant
Affiliation:
Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60208, USA
Stephen H. Davis
Affiliation:
Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60208, USA
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Abstract

Plane stagnation-point flow is modulated in the free stream so that the velocity components are proportional to KH + K cosωt. Similarity solutions of the Navier-Stokes equations are examined using high-frequency asymptotics for K and KH of unit order. Special attention is focused on the steady streaming generated in this flow with strongly non-parallel streamlines. For small modulation amplitude K [les ] KH, unique self-similar streaming flows exist. For large modulation amplitude K > KH, if (K/ω) (K/KH) [ges ] 1.661 no self-similar streaming is possible, while if 4/3 [les ] (K/ω) (K/KH) [les ] 1.661, then multiple steady solutions occur.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 198 , January 1989 , pp. 543 - 555
Copyright
1989 Cambridge University Press

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References

Grosch, C. E. & Salwen, H., 1982 Oscillating stagnation point flow. Proc. R. Soc. Lond. A 384, 175–190.Google Scholar
Grotberg, J. B.: 1984 Volume-cycled oscillatory flow in a tapered channel. J. Fluid Mech. 141, 249–264.Google Scholar
Hall, P.: 1974 Unsteady viscous flow in a pipe of slowly varying cross-section. J. Fluid Mech. 64, 209–226.Google Scholar
Ishigaki, M.: 1970 Periodic boundary layer near a two-dimensional stagnation point. J. Fluid Mech. 43, 477–486.Google Scholar
Lighthill, M. J.: 1954 The response of laminar skin friction and heat transfer to fluctuations in stream velocity. Proc. R. Soc. Lond. A 224, 1–23.Google Scholar
Longuet-Higgins, M. S.: 1953 Mass transport in water waves. Phil. Trans. R. Soc. Lond. A 245, 535–581.Google Scholar
Matunobu, Y.: 1977 Structure of pulsatile Hiemenz flow and temporal variations of wall shear stress near the stagnation point II. J. Phys. Soc. Japan 43, 326–329.Google Scholar
Morkovin, M. V.: 1978 Instability, transition to turbulence and predictability. AGARDograph no. 236.Google Scholar
Pedley, T. J.: 1972 Two-dimensional boundary layers in a free stream which oscillates without reversing. J. Fluid Mech. 55, 359–383.Google Scholar
Riley, N.: 1965 Oscillating viscous flows. Mathematika 12, 161–175.Google Scholar
Riley, N.: 1975 Unsteady laminar boundary layers. SIAM Rev. 17, 274–297.Google Scholar
Riley, N. & Weidman, P. D., 1989 Multiple solutions of the Falkner–Skan equation with a stretching boundary. SIAM J. Appl. Maths (to appear).Google Scholar
Rosenblat, S.: 1959 Torsional oscillations of a plane in a viscous fluid. J. Fluid Mech. 6, 206–220.Google Scholar
Rosenblat, S.: 1960 Flow between torsionally oscillating disks. J. Fluid Mech. 8, 388–391.Google Scholar
Rosenhead, L.: 1963 Laminar Boundary Layers. Oxford University Press.
Schlichting, H.: 1932 Berechnung ebener periodischer Grenzschichtströmungen. Phys. Z. 33, 327–335.Google Scholar
Schlichting, H.: 1960 Boundary Layer Theory. McGraw-Hill.
Secomb, T. W.: 1978 Flow in a channel with pulsating walls. J. Fluid Mech. 8, 273–288.Google Scholar
Stuart, J. T.: 1966 Double boundary layers in oscillatory viscous flow. J. Fluid Mech. 24, 673–687.Google Scholar