Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Stability of time-periodic temperature fields

Authors: Chia-Shun Yih and Jinsong Shi
Journal: Quart. Appl. Math. 45 (1987), 39-50
MSC: Primary 76E15
DOI: https://doi.org/10.1090/qam/885166
MathSciNet review: 885166
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The energy method developed by Joseph [4], Davis [2], and Homsy [3] is applied to the time-periodic temperature fields considered by Yih and Li [11] to obtain Rayleigh numbers below which the fluid is stable. This is done to see how far the Rayleigh numbers so determined fall below the critical Rayleigh numbers, above which the flow is unstable, as determined by the linear theory [11]. It is found that, unlike the case of classical Bénard cells, the gray area, or area of ignorance, is quite large, indicating the need for some improvement of the energy method to give sharper lower bounds on the Rayleigh number.

References [Enhancements On Off] (What's this?)

  • [1] S. Carmi, Energy stability of modulated flows, Phys. Fluids 17, 1951-1955 (1974)
  • [2] S. H. Davis, Buoyancy-surface tension instability by the method of energy, J. Fluid Mech. 39, 347-359 (1969)
  • [3] G. M. Homsy, Global stability of time-dependent flows: impulsively heated or cooled fluid layers, J. Fluid Mech. 60, 129-139 (1973)
  • [4] Daniel D. Joseph, Nonlinear stability of the Boussinesq equations by the method of energy, Arch. Rational Mech. Anal. 22 (1966), 163–184. MR 0192725, https://doi.org/10.1007/BF00266474
  • [5] D. D. Joseph, Stability of fluid motions, vols. I and II, Springer Verlag, 1976
  • [6] W. McF. Orr, The stability or instability of the steady motions of a perfect liquid and of a viscous liquid, Part I. A perfect liquid, and Part II, A viscous liquid, Proc. Roy. Irish Acad. Sect. A 27, 9-68 and 69-138 (1907)
  • [7] Anne Pellew and R. V. Southwell, On maintained convective motion in a fluid heated from below, Proc. Roy. Soc. London. Ser. A. 176 (1940), 312–343. MR 0003752, https://doi.org/10.1098/rspa.1940.0092
  • [8] O. Reynolds, On the dynamic theory of incompressible viscous fluid and the determination of the criterion, Philos. Trans .Roy. Soc. London Ser. A 186, 123-164 (1895)
  • [9] James Serrin, On the stability of viscous fluid motions, Arch. Rational Mech. Anal. 3 (1959), 1–13. MR 0105250, https://doi.org/10.1007/BF00284160
  • [10] J. T. Stuart, On the nonlinear mechanics of hydrodynamic stability, J. Fluid Mech. 4, 1-21 (1958)
  • [11] C.-S. Yih and C.-H. Li, Instability of unsteady flows or configurations, Part 2. Convective instability, J. Fluid Mech. 54, 143-152 (1972)

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 76E15

Retrieve articles in all journals with MSC: 76E15

Additional Information

DOI: https://doi.org/10.1090/qam/885166
Article copyright: © Copyright 1987 American Mathematical Society

Brown University The Quarterly of Applied Mathematics
is distributed by the American Mathematical Society
for Brown University
Online ISSN 1552-4485; Print ISSN 0033-569X
© 2017 Brown University
Comments: qam-query@ams.org
AMS Website