Long Wavelength Oscillatory Instability in Binary Fluids
Binary fluid convection takes the form of oscillations for sufficiently negative separation ratios. When the confining plates are of poor thermal conductivity these oscillations have a long wavelength. Nonlinear planform equations governing the resulting instability are derived for both two and three dimensions. The technique uses a multiple scale analysis combined with reconstitution. The validity of the resulting equations is discussed and compared with asymptotically exact alternatives. The results are found to differ demonstrating the failure of the reconstitution procedure.
KeywordsRayleigh Number Hopf Bifurcation Biot Number Critical Rayleigh Number Heteroclinic Cycle
Unable to display preview. Download preview PDF.
- T. Clune and E. Knobloch, Physica D, in press (1994).Google Scholar
- S. Cox, J. Eng. Math., in press (1994).Google Scholar
- S. Cox and S. Leibovich, preprint (1994).Google Scholar
- E. Knobloch, in Pattern Formation in Complex Dissipative Systems, S. Kai, ed., World Scientific, Singapore, pp. 263–274 (1992).Google Scholar
- J.W. Swift (1984), Ph.D. Thesis, University of California, Berkeley.Google Scholar