Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-25T05:22:00.886Z Has data issue: false hasContentIssue false
  • English
  • Français

Forced vertical oscillations in a viscous stratified fluid

Published online by Cambridge University Press:  24 October 2008

B. D. Dore
B. D. Dore
Affiliation:
Department of Mathematics, University of Reading
Get access Rights & Permissions [Opens in a new window]

Abstract

The linear fluid dynamics is considered when infinite vertical boundaries are set in oscillatory vertical motion. The case of exponential stratification with constant kinematic viscosity is explicitly studied. When the forcing frequency equals the Brunt–Vaisälä frequency for the fluid, the customary boundary layers are absent in the steady-state oscillation, however small be the kinematic viscosity; for a semi-infinite fluid the corresponding horizontal extent of the region influenced by the boundary motion is then of the order of the stratification length. The sign of the phase angle is everywhere dependent on whether the magnitude of the forcing frequency is greater than or less than that of the Brunt–Vaisäla frequency.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 66 , Issue 3 , November 1969 , pp. 617 - 627
Copyright
Copyright © Cambridge Philosophical Society 1969

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

REFERENCES

(1)Graebel, W. P., Long, R. R. and Wu, T. Y. T.Report on the International Conference on stratified fluids. J. Fluid Mech. 31 (1968), 689–703.Google Scholar
(2)Dore, B. D.The decay of oscillations of a non-homogeneous fluid within a container. Proc. Cambridge Philos. Soc. 65 (1969), 301–307.Google Scholar
(3)Schlichting, H. Chapter 5 of Boundary layer theory, pp. 75–76 (4th edition, McGraw-Hill, 1960).Google Scholar
(4)Carslaw, H. S. and Jaeger, J. C. Chapter 5 of Operational methods in applied mathematics, pp. 94–96 (2nd edition, Oxford University Press, 1948).Google Scholar
(5)Carslaw, H. S. and Jaeger, J. C. Chapter 3 of Conduction of heat in solids, p. 105 (2nd edition, Clarendon Press, 1959).Google Scholar
(6)Greenspan, H. S. Chapter 2 of The theory of rotating fluids, p. 30 (Cambridge University Press, 1968).Google Scholar