(NEED TO DERIVE EQUATION NOT JUST WORDS) In cartesian tangent plane coordinates, derive the horizontal divergence and the vertical vorticity of the geostrophic wind assuming (a) f is constant (b) f = 2Ωsin[φ0 +(y/Re)] where Re = radius of the Earth and the latitude φ = φ0 + y/Re. In order to avoid having to make assumptions about ρ, use the pressure-coordinate (i.e.geopotential) formulation for the geostrophic wind.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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(NEED TO DERIVE EQUATION NOT JUST WORDS) In cartesian tangent plane coordinates, derive the horizontal divergence and the vertical vorticity of the geostrophic wind assuming (a) f is constant (b) f = 2Ωsin[φ0 +(y/Re)] where Re = radius of the Earth and the latitude φ = φ0 + y/Re. In order to avoid having to make assumptions about ρ, use the pressure-coordinate (i.e.geopotential) formulation for the geostrophic wind.

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