Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-19T15:40:35.233Z Has data issue: false hasContentIssue false
  • English
  • Français

A wave-guide model for turbulent shear flow

Published online by Cambridge University Press:  28 March 2006

Marten T. Landahl
Marten T. Landahl
Affiliation:
Massachusetts Institute of Technology
Get access Rights & Permissions [Opens in a new window]

Abstract

It is shown that for a dynamical system admitting wave propagation modes (i.e. a wave-guide) the cross-power spectral density for stationary random fluctuations in the system will be dominated by the waves if they are lightly damped, the reason being that these can correlate over large distances of the order the inverse of the damping ratio. For a turbulent shear flow the wave propagation constant is obtained approximately from the solution of the Orr-Sommerfeld problem for the mean flow. Numerical calculations for a flat-plate boundary layer produce results for the streamwise dependence of the cross-power spectral density for the surface pressure fluctuations in good qualitative and quantitative agreement with measurements. An exception is the convection velocity for which the theory predicts a value that is somewhat too low.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 29 , Issue 3 , 6 September 1967 , pp. 441 - 459
Copyright
© 1967 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

Betchov, R. & Criminale, W. O. 1964 Oscillations of a turbulent flow. Phys. Fluids, 7, 12, 1920–1926.Google Scholar
Coles, D 1926 The law of the wake in the turbulent boundary layer J. Fluid Mech. 1, 191.Google Scholar
Corcos, G. M. 1964 The structure of the turbulent pressure field in boundary-layer flows J. Fluid Mech. 18, 353.Google Scholar
Eckhaus, W. 1965 Studies in Non-linear Stability Theory. Berlin: Springer-Verlag.
Greenspan, H. P. & Benney, D. J. 1963 On shear-layer instability breakdown and transition J. Fluid Mech. 15, 135.Google Scholar
Kaplan, R. E. 1964 The stability of laminar incompressible boundary layers in the presence of compliant boundaries. M.I.T. ASRL TR 116–1.Google Scholar
Kraichnan, R. H. 1956 Pressure fluctuations in turbulent flow over a flat plate J. Acoust. Soc. Am. 28, 378.Google Scholar
Landahl, M. T. 1965 A wave-guide model for turbulent shear flow. Nat. Aero. and Space Adm. Contractor Rept., NASA CR-317.Google Scholar
Landahl, M. T. 1966 A time-shared program system for the solution of the stability problem for parallel flows over rigid or flexible surfaces. Massachusetts Institute of Technology, Aeroelastic and Structures Research Laboratory Rept. no. 116–4.Google Scholar
Landahl, M. T. & Kaplan, R. E. 1965 The effect of compliant walls on boundary layer stability and transition. Agardograph, Paris 97, 1, 353.Google Scholar
Lighthill, M. T. 1952 On sound generated aerodynamically. Part I. Proc. Roy. Soc. A 211, 564.Google Scholar
Lilley, G. M. & Hodgson, T. H. 1960 On surface pressure fluctuations in turbulent boundary layers. AGARD Rept. no. 276.Google Scholar
Mack, L. M. 1965 The stability of the compressible laminar boundary layer according to a direct numerical solution. Agardograph, Paris 97, 1, 329.Google Scholar
Malkus, W. 1956 Outline of a theory of turbulent shear flow J. Fluid Mech. 1, 521.Google Scholar
Millikan, C. 1938 A critical discussion of turbulent flows in channels and circular tubes. Proc. 5th Int. Cong. Appl. Mech., Cambridge, p. 386.Google Scholar
Mollo-Christensen, E. L. 1967 Jet noise and shear-flow instability seen from an experimenter's viewpoint ASME J. Appl. Mech. 89, Ser. E, 1.Google Scholar
Reichardt, H. 1951 Vollständige Darstellung der turbulenten Geschwindigkeitsver-teilung in Glatten Leitungen Z. Angev. Math. Mech. 31, 208.Google Scholar
Reynolds, W. C. & Tiederman, W. G. 1967 Stability of turbulent channel flow, with application to Malkus's theory J. Fluid Mech. 27, 253.Google Scholar
Runstadler, P. W., Kline, S. J. & Reynolds, W. C. 1963 An experimental investigation of the flow structure of the turbulent boundary layer. Rept. MD-8, of Mechanical Engineering, Stanford University
Townsend, A. A. 1956 The Structure of Turbulent Shear Flow. Cambridge University Press.
Tu, B. J. & Willmarth, W. W. 1966 An experimental study of the structure of turbulence near the wall through correlation measurements in a thick boundary layer. Univ. of Michigan, O.R.A. Rept. no. 02920-3-T.Google Scholar
Willmarth, W. W. & Roos, F. W. 1965 Resolution and structure of the wall pressure field beneath a turbulent boundary layer J. Fluid Mech. 22, 81.Google Scholar
Willmarth, W. W. & Wooldridge, C. E. 1962 Measurements of the fluctuating pressure at the wall beneath a thick turbulent boundary layer J. Fluid Mech. 14, 187.Google Scholar