Montgomery Potential

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The Montgomery potential is an abstract quantity that is used in numerical weather and climate models to simulate wind currents. The Montgomery Potential depends on two variables, geopotential and temperature .

${\displaystyle \mathbf {M} =\Phi +c_{p}T=gz+c_{p}T}$

• ${\displaystyle \mathbf {M} }$ denotes the Montgomery Potential

• ${\displaystyle \Phi \,}$is the same and denotes the geopotential . ${\displaystyle gz\,}$

• ${\displaystyle c_{p}\,}$is the specific heat of dry air at constant pressure

• ${\displaystyle T\,}$denotes the temperature

• ${\displaystyle g\,}$refers to the acceleration due to gravity

• ${\displaystyle z\,}$ is the height

The acceleration of the air particles in the x or y direction can be derived from the gradient of the Montgomery potential. In the example below, the wind vector u (speed vector in the x direction) changes over time depending on the gradient of the Montgomery potential in the x direction. It is a rewritten momentum equation . The subscript indicates that we are moving in the theta level, i.e. the potential temperature is constant. If the Montgomery potential remains constant in the x-direction and if we neglect the Coriolis parameter f, the wind speed u does not change with time t. ${\displaystyle \theta \,}$

${\displaystyle {Du \over Dt}-fv=-\left({\partial M \over \partial x}\right)_{\theta }}$

• ${\displaystyle u\,}$ Velocity vector in the x direction

• ${\displaystyle v\,}$ Velocity vector in y-direction

• ${\displaystyle f\,}$denotes the Coriolis parameter . It depends on the geographical latitude and is 0 at the equator and reaches its maximum at the poles.

• ${\displaystyle \theta \,}$is the potential temperature