Editing Primitive equations (section)

==Forces that cause atmospheric motion==
[[Force]]s that cause atmospheric motion include the [[pressure gradient]] force, [[gravity]], and [[viscous]] [[friction]].  Together, they create the forces that accelerate our atmosphere.

The pressure gradient force causes an acceleration forcing air from regions of high pressure to regions of low pressure. Mathematically, this can be written as:

:<math>\frac{f}{m} = \frac{1}{\rho} \frac{dp}{dx}.</math>

The gravitational force accelerates objects at approximately 9.8&nbsp;m/s<sup>2</sup> directly towards the center of the Earth.

The force due to viscous friction can be approximated as:

:<math>f_r = {f \over a} {1 \over \rho}
\mu\left(\nabla\cdot(\mu \nabla v) + \nabla(\lambda\nabla\cdot v) \right). </math>

Using Newton's second law, these forces (referenced in the equations above as the accelerations due to these forces) may be summed to produce an equation of motion that describes this system. This equation can be written in the form:

:<math>\frac{dv}{dt} = - (\frac{1}{\rho}) \nabla p - g(\frac{r}{r}) + f_r</math>
<!-- What is the r/r term here? -->

:<math>g = g_e. \,</math>

Therefore, to complete the system of equations and obtain 6 equations and 6 variables:
*<math>\frac{dv}{dt} = - (\frac{1}{\rho})\nabla p - g(\frac{r}{r}) + (\frac{1}{\rho})\left[\nabla\cdot (\mu \nabla v) + \nabla(\lambda \nabla\cdot v)\right]</math>
<!-- What is the r/r term here? -->
*<math>c_{v} \frac{dT}{dt} + p \frac{d\alpha}{dt} = q + f</math>
*<math>\frac{d\rho}{dt} + \rho\nabla\cdot v = 0</math>
*<math>p = n T.</math>

where n is the [[number density]] in mol, and T:=RT is the temperature equivalent value in Joule/mol.