Hostname: page-component-745bb68f8f-d8cs5 Total loading time: 0 Render date: 2025-02-02T00:51:38.188Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on an algebraic instability of inviscid parallel shear flows

Published online by Cambridge University Press:  19 April 2006

M. T. Landahl
M. T. Landahl
Affiliation:
Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA, U.S.A. and Department of Mechanics, The Royal Institute of Technology, Stockholm, Sweden
Get access Rights & Permissions [Opens in a new window]

Abstract

It is shown that all parallel inviscid shear flows of constant density are unstable to a wide class of initial infinitesimal three-dimensional disturbances in the sense that, according to linear theory, the kinetic energy of the disturbance will grow at least as fast as linearly in time. This can occur even when the disturbance velocities are bounded, because the streamwise length of the disturbed region grows linearly with time. This finding may have implications for the observed tendency of turbulent shear flows to develop a longitudinal streaky structure.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 98 , Issue 2 , 29 May 1980 , pp. 243 - 251
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

Arnol'd, V. I. 1965 Sov. Math. 6, 773.
Case, K. M. 1960 Phys. Fluids 3, 143.
Chimonas, G. 1979 J. Fluid Mech. 90, 1.
Drazin, P. G. & Howard, L. N. 1966 Adv. Appl. Math. 9, 1.
Eliassen, A., Høiland, J. & Riis, E. 1953 Inst. for Weather & Climate Res. Publ. no. 1, Oslo.
Ellingsen, T. & Palm, E. 1975 Phys. Fluids 18, 487.
Fjørtoft, R. 1950 Geophys. Publ. 17, no. 1, Oslo.
Gustavsson, L. H. 1978 Dept. of Mech. Roy. Inst. Tech. Rep. TRITA-MEK-78-02, Stockholm.
Heisenberg, W. 1924 Ann. Phys. Leipzig 24, 577.
Howard, L. N. 1961 J. Fluid Mech. 10, 509.
Landahl, M. T. 1977 Phys. Fluids Suppl. 20, 55.
Lin, C. C. 1955 The Theory of Hydrodynamic Stability. Cambridge University Press.
Orr, W. M. F. 1907 Proc. Roy. Irish Acad. A 17, 124.
Rayleigh, Lord 1880 Proc. Lond. Math. Soc. 9, 57.
Stuart, J. T. 1965 N.P.L. Aero Rep. 1147; AGARD Rep. 514.
Titschmarsh, E. C. 1939 The theory of Functions, 2d edn. Oxford University Press.
Wilke, L. H. 1967 J. Math. & Phys. 46, 151.