Journal of the Australian Mathematical Society - Series B
Vol. 40 Part 2 (1998)

Strongly nonlinear vortices in magnetized ferrofluids

Craig L. Russell
School of Chemistry, Macquarie University, NSW 2109, Australia.
P. J. Blennerhassett
School of Mathematics, University of New South Wales, NSW 2052, Australia.
P. J. Stiles
School of Chemistry, Macquarie University, NSW 2109, Australia.


Nonlinear convective roll cells that develop in thin layers of magnetized ferrofluids heated from above are examined in the limit as the wavenumber of the cells becomes large. Weakly nonlinear solutions of the governing equations are extended to solutions that are valid at larger distances above the curves of marginal stability. In this region, a vortex flow develops where the fundamental vortex terms and the correction to the mean are determined simultaneously rather than sequentially. The solution is further extended into the nonlinear region of parameter space where the flow has a core-boundary layer structure characterized by a simple solution in the core and a boundary layer containing all the harmonics of the vortex motion. Numerical solutions of the boundary layer equations are presented and it is shown that the heat transfer across the layer is significantly greater than in the conduction state.

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