# Instability of Time-Periodic Flows

## Abstract

The instabilities of some spatially and/or time-periodic flows are discussed, in particular flows with curved streamlines which can support Taylor-Görtler vortices are described in detail. The simplest flow where this type of instability can occur is that due to the torsional oscillations of an infinitely long circular cylinder. For more complicated spatially varying time-periodic flows a similar type of instability can occur and is spatially localized near the most unstable positions. When nonlinear effects are considered it is found that the instability modifies the steady streaming boundary layer induced by the oscillatory motion. It is shown that a rapidly rotating cylinder in a uniform flow is susceptible to a related type of instability; the appropriate stability equations are shown to be identical to those which govern the instability of a Boussinesq fluid of Prandtl number unity heated time periodically from below.

## Keywords

Rayleigh Number Neutral Curve Secondary Instability Taylor Number Taylor Vortex## Preview

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## References

- [1]Chandrasehkar, S., 1963, Hydrodynamic and Hydromagnetic Stability, Dover.Google Scholar
- [2]Duck, P. w. and Hall, P., 1981, ZAMP,
**32**, p. 102.MathSciNetADSzbMATHCrossRefGoogle Scholar - [3]Glauert, M. B., 1957, J. Fluid Mech.,
**2**, p. 89.MathSciNetADSzbMATHCrossRefGoogle Scholar - [4]Hall, P., 1981, J. Fluid Mech.,
**105**, p. 523.ADSzbMATHCrossRefGoogle Scholar - [5]Hall, P., 1984, J. Fluid Mech.,
**146**, p. 347.ADSzbMATHCrossRefGoogle Scholar - [6]Honji, H., 1981, J. Fluid Mech.,
**107**, p. 509.ADSCrossRefGoogle Scholar - [7]Moore, D. W., 1957, J. Fluid Mech.,
**2**, p. 541.MathSciNetADSzbMATHCrossRefGoogle Scholar - [8]Park, K., Barenghi, C., and Donnelly, R. J., 1980, Physics Letters,
**78a**, p. 152.ADSGoogle Scholar - [9]
- [10]Riley, N., 1967, J. Inst. Math. Appls.,
**3**, p. 419.zbMATHCrossRefGoogle Scholar - [11]Schlichting, H., 1932, Phys. z.,
**33**, p. 327.Google Scholar - [12]Seminara, G. and Hall, P., 1976, PRS(A),
**350**, p. 299.zbMATHGoogle Scholar - [13]Seminara, G. and Hall, P., 1977, PRS(A),
**354**, p. 119.zbMATHGoogle Scholar - [14]Soward, A. and Jones, C., 1983, QJMAM,
**36**, p. 19.MathSciNetzbMATHGoogle Scholar - [15]Stuart, J. T., 1966, J. Fluid Mech.,
**24**, p. 673.MathSciNetADSzbMATHCrossRefGoogle Scholar