# Poisson equation

From Glossary of Meteorology

## Poisson equation

- The partial differential equationwhere ∇
^{2}is the Laplacian operator, φ a scalar function of position, and*F*a given function of the independent space variables.

For the special case*F*= 0, the Poisson equation reduces to the Laplace equation.*See*relaxation method.

- The relationship between temperature
*T*and pressure*p*of an ideal gas undergoing an adiabatic process; given bywhere*T*_{0}and*p*_{0}are initial state values and κ is the Poisson constant. With*p*_{0}given as a reference pressure of 100 kPa,*T*_{0}is equal to the potential temperature.