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Nonlinear convection in the boundary layer above a sinusoidally heated flat plate
The thermal boundary layer induced within a horizontal semi-infinite layer of Boussinesq fluid by a sinusoidally heated bounding plate is known to be susceptible to vortex instability. The structure of short wavelength convection is considered here and the analysis taken from linear, through weakly nonlinear and onto the fully nonlinear stage. At this point the activity is sufficiently strong that it induces large changes in the underlying thermal profile and the overall flow characteristics are determined by the solution of a free boundary-value problem. This solution demonstrates that the highly nonlinear vortices tend to settle into a periodic form in which intervals of intense activity alternate with times of relative quiescence.
History
Publication title
Quarterly Journal of Mechanics and Applied MathematicsVolume
53Pagination
475-495ISSN
0033-5614Department/School
School of Natural SciencesPublisher
Oxford Univ PressPlace of publication
Great Clarendon St, Oxford, England, Ox2 6DpRights statement
Copyright Oxford University Press 2000Repository Status
- Restricted