Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 344 / 3 / c / i

Table of contents
- Solution i

Solution

For a uniform field,

v \cdot \nabla p = 0

, and the stated flow has

Ω = 0

and

D \cdot p = γ (p_{x}, - p_{y} /2, - p_{z} /2) .

D p / D t = - Γ h

becomes

\partial_{t} p = - Γ [h - \frac{ξ γ}{Γ} (p_{x}, - p_{y} /2, - p_{z} /2)] .

Thus

h = h + α (p_{x}, - p_{y} /2, - p_{z} /2), α = - \frac{ξ γ}{Γ} .

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