Someone argues: "The sea breeze starts from still air

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Kinematics, conservation laws and ideal flow · Convection, rotation and geophysical flows

Fluid Dynamics, Ch Vorticity: its sources, its field and the motion of vortices

Problem

Someone argues: "The sea breeze starts from still air, and still air has zero circulation around any circuit. Kelvin's circulation theorem states that the circulation around a material circuit is conserved for an inviscid, barotropic fluid under conservative body forces, and the coastal air is inviscid to a good approximation and gravity is conservative, so the circulation must stay zero forever. The sea breeze cannot begin." ((a)) Find the error in this reasoning. ((b)) Use Bjerknes's circulation theorem,

\mathrm{d}\Gamma/\mathrm{d}t = R\ln(p_1/p_2)\,\Delta T

, to find the actual initial rate of gain of circulation around a rectangular coastal circuit

20\,\mathrm{km}

wide between the

1000\,\mathrm{hPa}

and

950\,\mathrm{hPa}

levels, with the land

\Delta T = 6\,\mathrm{K}

warmer than the sea, taking the specific gas constant of air as

R=287\,\mathrm{J\,kg^{-1}\,K^{-1}}

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