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where
is the
Coriolis parametercomponent of the Earth's rotation parallel to the force of gravity,
is the azimuthal velocity,
is height and
is radius from the tank center.
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The Fronts experiment introduces temperature gradients as an important factor leading to pressure gradients. As a consequence of hydrostatic and geostrophic balance, temperature gradients cause vertical wind shear according to the relation
| LaTeX Math Block |
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\frac{\partial \mathbf{u}_g}{\partial z} = -\frac{R\alpha g}{f p} \hat{\mathbf{z}} \times \nabla pT |
where
is the speed vector, is the thermal expansivity of the fluid, is the Coriolis parameter, and is temperature. This expression holds only for incompressible fluids, so is valid for the tank experiment: for comressible fluids like the atmosphere we rewrite the equation in pressure coordinates instead of height. General Circulation in the Atmosphere
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