Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-19T03:54:38.127Z Has data issue: false hasContentIssue false
  • English
  • Français

On the stability of fine-scaled turbulent free shear flows

Published online by Cambridge University Press:  19 April 2006

Hartmut H. Legner  and
Michael L. Finson
Hartmut H. Legner
Affiliation:
Avco Everett Research Laboratory, Inc., Everett, Massachusetts Present address: Physical Sciences Inc., Woburn, Massachusetts.
Michael L. Finson
Affiliation:
Avco Everett Research Laboratory, Inc., Everett, Massachusetts Present address: Physical Sciences Inc., Woburn, Massachusetts.
Get access Rights & Permissions [Opens in a new window]

Abstract

A theoretical model has been developed to investigate the stability of a disturbance in an incompressible turbulent shear flow dominated by turbulence scales that are small with respect to the cross-stream dimension of the flow. The approach utilizes the ‘phase average’ concept to derive the differential equations governing the mechanics of a potential flow disturbance. Turbulence closure is effected at second order. The result is an Orr–Sommerfeld-type equation with complications introduced by the turbulence model. Integration of the linear eigenvalue problem for a wake disturbance leads to the result that the critical eddy-viscosity-based Reynolds number is markedly increased by decreasing the turbulence scale. The viscoelastic behaviour of background turbulence, further complicated by the effects of mean shear, appears to provide stabilization and is discussed in some detail.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 100 , Issue 2 , 25 September 1980 , pp. 303 - 319
Copyright
© 1980 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

Avidor, J. M. & Schneiderman, A. M. 1975 A.I.A.A. J. 13, 485.
Berenak, L. L. 1960 Noise Reduction, pp. 661–664. McGraw-Hill.
Betchov, R. 1966 Aerospace Corp. Rep. no. TR-669 (9220-02).
Betchov, R. & Criminale, W. O. 1965 Stability of Parallel Flows, p. 275. Academic.
Bradshaw, P. 1966 J. Fluid Mech. 26, 775.
Brown, G. L. & Roshko, A. 1974 J. Fluid Mech. 64, 775.
Champagne, F. H., Harris, V. G. & Corrsin, S. 1970 J. Fluid Mech. 41, 81.
Clark, A. R. & Hussain, A. K. M. F. 1979 On convection velocities in a mixing layer: effects of initial condition. In Turbulent Shear Flows, pp. 230–235. Imperial College, London.
Crow, S. C. 1968 J. Fluid Mech. 33, 1.
Elswick, R. C. 1971 Wave-induced Reynolds stress in turbulent shear layer stability. Ph.D. thesis, The Pennsylvania State University, University Park, Pennsylvania.
Finson, M. L. 1973 A.I.A.A. J. 11, 1137.
Hanjalic, K. & Launder, B. 1972 J. Fluid Mech. 52, 609.
Husain, Z. D. & Hussain, A. K. M. F. 1979 A.I.A.A. J. 17, 48.
Hussain, A. K. M. F. & Clark, A. R. 1977 Phys. Fluids 20, 1416.
Hussain, A. K. M. F. & Reynolds, W. C. 1970a J. Fluid Mech. 41, 291.
Hussain, A. K. M. F. & Reynolds, W. C. 1970b Dept. Mech. Engng Rep. RM-6, Stanford Univ., California.
Hussain, A. K. M. F. & Reynolds, W. C. 1972 J. Fluid Mech. 54, 241.
Hussain, A. K. M. F. & Zedan, M. F. 1978a Phys. Fluids 21, 1100.
Hussain, A. K. M. F. & Zedan, M. F. 1978b Phys. Fluids 21, 1475.
Launder, B. E., Reece, G. J. & Rodi, W. 1975 J. Fluid Mech. 68, 537.
Mollo-christensen, E. 1971 A.I.A.A. J. 9, 1217.
Ng, K. H. & Spalding, B. D. 1972 Phys. Fluids 15, 20.
Phillips, O. M. 1966 The Dynamics of the Upper Ocean, p. 87. Cambridge University Press.
Radbill, J. R. & Mccue, G. A. 1970 Quasilinearization and Non-Linear Problems in Fluid and Orbital Mechanics, p. 114. Elsevier.
Reynolds, W. C. 1972 J. Fluid Mech. 54, 481.
Reynolds, W. C. & Hussain, A. K. M. F. 1972 J. Fluid Mech. 54, 263.
Rotta, J. 1951 Z. Phys. 129, 547; 131, 51.
Townsend, A. A. 1956 The Structure of Turbulent Shear Flow. Cambridge University Press.