Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-18T19:00:38.576Z Has data issue: false hasContentIssue false
  • English
  • Français

On the receptivity of free shear layers to two-dimensional external excitation

Published online by Cambridge University Press:  21 April 2006

Thomas F. Balsa
Thomas F. Balsa
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, AZ 85721, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper, we study the receptivity of a typical free shear layer to pulse-type and periodic excitation. We do this by solving the initial-value problem completely and studying its long-time behaviour. This leads to a wave packet for the pulse. By the superposition of many wave packets, we generate a spatial instability mode when the flow is convectively unstable. This establishes a general and simple relationship between the receptivities for pulse-type and sinusoidal excitations. We find that a shear layer is very receptive to high-frequency disturbances that are generated near the centreline of the layer.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 187 , February 1988 , pp. 155 - 177
Copyright
© 1988 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

Balsa, T. 1987 On the spatial instability of piecewise linear free shear layers. J. Fluid Mech. 174, 553–563.Google Scholar
Betchov, R. & Criminale, W. O. 1966 Spatial instability of the inviscid jet and wake. Phys. Fluids 9, 359–362.Google Scholar
Betchov, R. & Criminale, W. O. 1967 Stability of Parallel Flows. Academic.
Bleistein, N. & Handelsman, R. 1975 Asymptotic Expansion of Integrals. Holt, Rinehart and Winston.
Craik, A. D. D. & Criminale, W. O. 1986 Evolution of wavelike disturbances in shear flows: a class of exact solutions of the Navier-Stokes equations. Proc. R. Soc. Lond. A 406, 13–26.Google Scholar
Criminale, W. O. & Kovasznay, L. G. 1962 The growth of localized disturbances in a laminar boundary layer. J. Fluid Mech. 12, 59–80.Google Scholar
Drazin, P. G. & Reid, W. H. 1981 Hydrodynamic Stability. Cambridge University Press.
Duff, G. F. D. & Naylor, D. 1966 Differential Equations of Applied Mathematics. Wiley.
Farrell, B. F. 1982 The initial growth of disturbances in a baroclinic flow. J. Atmos. Sci. 38, 1663–1686.Google Scholar
Farrell, B. F. 1984 Modal and non-modal baroclinic waves. J. Atmos. Sci. 41, 668–673.Google Scholar
Gaster, M. 1968 The development of three-dimensional wave packets in a boundary layer. J. Fluid Mech. 32, 173–184.Google Scholar
Gaster, M. 1975 A theoretical model of a wave packet in the boundary layer on a flat plate. Proc. R. Soc. Lond A 347, 271–289.Google Scholar
Gaster, M., Kit, E. & Wygnanski, I. 1985 Large-scale structures in a forced turbulent mixing layer. J. Fluid Mech. 150, 23–39.Google Scholar
Glezer, A., Wygnanski, I. & Balsa, T. 1986 Spatial and temporal evolution of momentary disturbances in an excited turbulent mixing layer. Butt. Am. Phys. Soc. 31, 1694 (abstract only).Google Scholar
Goldstein, M. E. 1983 The evolution of Tollmien-Schlichting waves near a leading edge. J. Fluid Mech. 127, 59–81.Google Scholar
Greenspan, H. P. & Benney, D. 1963 On shear-layer instability, breakdown and transition. J. Fluid Mech. 15, 133–153.Google Scholar
Huerre, P. & Monkewitz, P. 1985 Absolute and convective instabilities in free shear layers. J. Fluid Mech. 159, 151–168.Google Scholar
Mattingly, G. E. & Criminale, W. O. 1972 The stability of an incompressible two-dimensional wake. J. Fluid Mech. 51, 233–272.Google Scholar
Michalke, A. 1964 On the inviscid instability of the hyperbolic-tangent velocity profile. J. Fluid Mech. 19, 543–556.Google Scholar
Michalke, A. 1965 On spatially growing disturbances in an inviscid shear layer. J. Fluid Mech. 23, 521–544.Google Scholar
Tatsumi, T., Gotoh, K. & Ayukawa, K. 1964 The stability of a free boundary layer at large Reynolds numbers. J. Phys. Soc. Japan 19, 1966–1980.Google Scholar