Rossby radius of deformation

The distance that cold pools of air can spread under the influence of the Coriolis force.

A cold pool will initially spread out toward and under warmer air because of higher pressure under the cold, denser air. However, as the spreading velocity increases, the Coriolis force will increasingly turn the velocity vector until it is parallel, rather than perpendicular, to the pressure gradient. At this point, no further spreading will occur and the winds will be in geostrophic equilibrium. The final equilibrium distance traveled by the edge of the cold air equals the external Rossby radius of deformation, λ_R:
where g is gravitational acceleration, H is the initial depth of the cold pool, Δθ is the potential temperature contrast between the cold and surrounding warm air, θ₀ is the absolute potential temperature of the warm air, and f_c is the Coriolis parameter.
An internal Rossby radius of deformation can be defined for fluids with a gradient of potential temperature rather than a temperature interface:
where N_BV is the average Brunt–Väisälä frequency within the troposphere and Z_T is the depth of the troposphere.

This radius is important for determining the phase speed and wavelength of baroclinic waves (Rossby waves) in the general circulation. An alternative definition for internal Rossby radius of deformation is
where G is the geostrophic wind speed and z_i is the depth of the atmospheric boundary layer, approximated here as z_i = G/N_BV. This form is useful in determining boundary layer (Ekman) pumping through the top of the boundary layer.

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