Rooms are sometimes heated by radiators (hot surfaces) that have no associated blowers or fans. Suppose that, in a room whose air is perfectly still, a radiator is turned on to high temperature. The air will begin to circulate (convect), and that air motion contains vorticity. Explain how the vorticity is generated in terms of the −∫dP/ρ term of Kelvin’s theorem (14.14) and the (−∇P × ∇ρ)/ρ² term of the vorticity evolution equation (14.6).

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Do Dt VP x Vp p² +vV². (14.6)