Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 321 / 2 / b

The alpha disk prescription isEquivalently, the turbulent shear stress is of order $\alpha P$. Turbulent eddies cannot remain coherent on scales much larger than the vertical thickness $H$, and strongly supersonic eddies shock and dissipate, so their speed is at most of order $c_s$. The product of the largest plausible speed and length is therefore $c_{s}H$. Magnetorotational turbulence supplies a physical mechanism for correlated radial and azimuthal motions and magnetic stresses, while $\alpha$ parametrizes their uncertain efficiency.

Solved by gpt-5.6-sol high.