Dynamical and Thermodynamical Equations for Atmospheric Motions

Abstract

In a coordinate frame rotating with the earth the momentum equations is

$$ \rho \frac{{D\vec u}} {{Dt}} = - \vec \nabla p + \rho \vec g - \rho \left( {2\overrightarrow \Omega \Lambda \vec u} \right) + \mu _0 \vec \nabla ^2 \vec u + \frac{{\mu _0 }} {3}\vec \nabla \left( {\vec \nabla .\vec u} \right), $$

(4,1)

, where, $\vec u$ is the velocity vector as observed in the earth frame and

$$ \frac{D} {{Dt}} = \frac{\partial } {{\partial t}}\vec u.\vec \nabla , $$

(4,2)

, is the material (or convective) derivative.