Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-18T21:58:17.968Z Has data issue: false hasContentIssue false
  • English
  • Français

The large amplitude motion of a liquid-filled gyroscope and the non-interaction of inertial and Rossby waves

Published online by Cambridge University Press:  29 March 2006

W. E. Scott
W. E. Scott
Affiliation:
U.S. Army Ballistic Research Laboratories and Department of Earth and Planetary Sciences, The Johns Hopkins University, Baltimore, Maryland 21218
Get access Rights & Permissions [Opens in a new window]

Abstract

An attempt is made to explain theoretically two curious phenomena involving the motion of the liquid in a spinning, gyrating, liquid-filled gyroscope. One of the phenomena is the periodic breakdown of the free-surface wave form of the spinning liquid in the gyroscope when it gyrates at angles larger than about 1°. The other is the resonant amplitude growth rate of the liquid-filled gyroscope at these angles, for then the small angle stability theory of Stewartson (1959) fails to make the correct predictions.

The analysis exploits the experimental fact that the axis of rotation of liquid in the rotor of a spinning gyrating gyroscope does not remain coincident with the axis of rotation of the rotor when the gyroscope gyrates at amplitudes greater than the above-mentioned 1°. It is shown that this lack of coincidence generates Rossby waves and modifies the inertial wave frequencies that would ordinarily occur in a right circular cylinder. There is no nonlinear interaction between these Rossby and inertial waves; hence the free-surface breakdown remains unexplained. However, the modification of the inertial wave frequencies does seem to account for the curious amplitude growth rate.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 72 , Issue 4 , 23 December 1975 , pp. 649 - 660
Copyright
© 1975 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

Greenspan, H. P. 1969 J. Fluid Mech. 36, 257.
Pedlosky, J. & Greenspan, H. P. 1967 J. Fluid Mech. 27, 291.
Stewartson, K. 1959 J. Fluid Mech. 5, 577.