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In the 1950s, the first successful programs for numerical weather forecasting utilized that equation. In modern numerical weather forecasting models and general circulation models (GCMs), vorticity may be one of the predicted variables, in which case the corresponding time-dependent equation is a prognostic equation.
The vorticity equation of fluid dynamics describes the evolution of the vorticity ω of a particle of a fluid as it moves with its flow; that is, the local rotation of the fluid (in terms of vector calculus this is the curl of the flow velocity). The governing equation is:
In the context of meteorology, a solenoid is a tube-shaped region in the atmosphere where isobaric (constant pressure) and isopycnal (constant density) surfaces intersect, causing vertical circulation. [1] [2] They are so-named because they are driven by the solenoid term of the vorticity equation. [3]
Hence from the knowledge of vorticity field, the operator can be inverted and the stream function can be calculated. In this particular case (equation 21), vorticity gives all the information needed to deduce motions, or streamfunction, thus one can think in terms of vorticity to understand the dynamics of the fluid.
While geostrophic motion refers to the wind that would result from an exact balance between the Coriolis force and horizontal pressure-gradient forces, [1] quasi-geostrophic (QG) motion refers to flows where the Coriolis force and pressure gradient forces are almost in balance, but with inertia also having an effect.
The Sverdrup relation can be derived from the linearized barotropic vorticity equation for steady motion: = / . Here is the geostrophic interior y-component (northward) and is the z-component (upward) of the water velocity. In words, this equation says that as a vertical column of water is squashed, it moves toward the Equator; as it is ...
In general, the evolution of vorticity can be broken into contributions from advection (as vortex tubes move with the flow), stretching and twisting (as vortex tubes are pulled or twisted by the flow) and baroclinic vorticity generation, which occurs whenever there is a density gradient along surfaces of constant pressure.
Q-vectors can be determined wholly with: geopotential height and temperature on a constant pressure surface.Q-vectors always point in the direction of ascending air. For an idealized cyclone and anticyclone in the Northern Hemisphere (where <), cyclones have Q-vectors which point parallel to the thermal wind and anticyclones have Q-vectors that point antiparallel to the thermal wind