A warm front in the Northern Hemisphere has air warmer to the south than to the north

PHYSICS · Multi-part · Fermi University Physics · Earth, Climate & Energy Physics · Atmosphere and ocean dynamics · Atmosphere and ocean dynamics

Fluid Dynamics, Ch Stratified flow, double diffusion and geophysical scales

Problem

A warm front in the Northern Hemisphere has air 6.0 K6.0\,\mathrm{K} warmer 300 km300\,\mathrm{km} to the south than to the north, at mean temperature T=280 KT = 280\,\mathrm{K}. The Coriolis parameter is f=1.0×10−4 s−1f = 1.0\times10^{-4}\,\mathrm{s^{-1}} and the flow is in geostrophic and hydrostatic balance (the thermal-wind approximation). ((a)) Calculate the magnitude of the vertical shear of the geostrophic wind, ∂ug/∂z\partial u_g/\partial z, implied by this temperature gradient. ((b)) State, in one sentence, whether the westerly wind increases or decreases with height, given that warm air lies to the south.

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