Strongly nonlinear vortices in magnetized ferrofluids

Nonlinear convective roll cells that develop in thin layers of magnetized f errofluids heated from above are examined in the limit as the wavenumber of the cells becomes large. Weakly nonlinear solutions of the governing equat ions 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-boun dary layer structure characterized by a simple solution in the core and a b oundary layer containing all the harmonics of the vortex motion. Numerical solutions of the boundary layer equations are presented and it is shown tha t the heat transfer across the layer is significantly greater than in the c onduction state.