Reduction of the complete omega equation to the simplest form

Summary

Using the vorticity and the thermodynamic equation, ‘Omega Equation’ has been derived. The effect of friction is not taken into account. The vertical velocity omega (ω) is composed of two parts, viz. mean baroclinicity in the atmosphere and heating. The baroclinicity part includes three terms. The magnitude of the second term is of the order of 10⁻¹⁰ to 10⁻¹² mb⁻¹ sec⁻²,and that of the last is 10⁻¹⁰ to 10⁻¹² mb⁻¹ sec⁻², whereas the first term is of the order of the vertical velocity omega 10⁻⁴ to 10⁻⁶ sec⁻¹. Therefore, the higher order terms can be omitted. Thus with the above approximation the complicated expression for omega is reduced to a simple form.