Past exam of the mathematics course of the University of Cambridge / 2022 / ib / Paper 3 / 16C / d

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- Solution d

Solution

The vorticity is normal to the plane, so the stretching term vanishes. Axisymmetry also makes angular advection vanish, and part (a) gives no radial advection. Hence the scalar vorticity equation is the radial diffusion equation

\frac{\partial ω}{\partial t} = ν (\frac{\partial ^{2} ω}{\partial r ^{2}} + \frac{1}{r} \frac{\partial ω}{\partial r}) .

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