Omega equation

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Published on July 29, 2021 2:23:55 PM ● Video Link: https://www.youtube.com/watch?v=isaulsgJfyo

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The omega equation is a culminating result in synoptic-scale meteorology. It is an elliptic partial differential equation, named because its left-hand side produces an estimate of vertical velocity, customarily expressed by symbol



ω


{\displaystyle \omega }
, in a pressure coordinate measuring height the atmosphere. Mathematically,



ω
=



d
p


d
t





{\displaystyle \omega ={\frac {dp}{dt}}}
, where





d

d
t





{\displaystyle {d \over dt}}
represents a material derivative. The underlying concept is more general, however, and can also be applied to the Boussinesq fluid equation system where vertical velocity is



w
=



d
z


d
t





{\displaystyle w={\frac {dz}{dt}}}
in altitude coordinate z.

Source: https://en.wikipedia.org/wiki/Omega_equation
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