Reconnaissance data for a hurricane give a wind that is very nearly horizontal and…

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Fluids & Continuum Physics · Kinematics, conservation laws and ideal flow

Fluids and Continuum Physics, Ch Vorticity, circulation and vortex motion

Problem

Reconnaissance data for a hurricane give a wind that is very nearly horizontal and blowing anticlockwise round the eye (viewed from above, with zz upward, so anticlockwise is positive). At a radius of 30 km30\ \mathrm{km} from the centre the wind speed is 45 m s−145\ \mathrm{m\,s^{-1}}, and the flow may be taken as steady and axisymmetric, so that the wind at that radius is everywhere tangential and of that speed. ((a)) Estimate the circulation round the horizontal circle of radius 30 km30\ \mathrm{km} centred on the eye. ((b)) Hence estimate the average vertical component of vorticity, ωz\omega_z, over the horizontal disc bounded by that circle.

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