Editing Primitive equations (section)

==Solution to the linearized primitive equations==
The [[analytic solution]] to the linearized primitive equations involves a sinusoidal oscillation in time and longitude, modulated by [[coefficient]]s related to height and latitude.

:<math> \begin{Bmatrix}u, v, \Phi \end{Bmatrix} = \begin{Bmatrix}\hat u, \hat v, \hat \Phi \end{Bmatrix} e^{i(s \lambda + \sigma t)} </math>

where ''s'' and <math>\sigma</math> are the zonal [[wavenumber]] and [[angular frequency]], respectively. The solution represents [[atmospheric waves]] and [[tides]].

When the coefficients are separated into their height and latitude components, the height dependence takes the form of propagating or [[evanescent waves]] (depending on conditions), while the latitude dependence is given by the [[Hough function]]s.

This analytic solution is only possible when the primitive equations are linearized and simplified. Unfortunately many of these simplifications (i.e. no dissipation, isothermal atmosphere) do not correspond to conditions in the actual atmosphere. As a result, a [[numerical solution]] which takes these factors into account is often calculated using [[general circulation model]]s and [[climate models]].