The Non-Monotonicity of Solutions in Swirling Flow.
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WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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The existence of solutions of Batchelors nonlinear differential equations for swirling flow induced by two parallel rotating coaxial discs of infinite size is investigated. It is found that if the discs rotate in the same direction with one rotating and one stationary disc as a special case, then for sufficiently small kinematic viscosity of the fluid, the angular velocity of the swirling flow cannot vary monotonically in the axial direction. Should a condition of monotonic variation of the angular velocity be imposed, then a solution to the governing differential equations would not exist. A detailed step by step proof is provided.
- Numerical Mathematics
- Fluid Mechanics