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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]
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 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.
Carl Rossby proposed in 1939 [4] that, instead of the full three-dimensional vorticity vector, the local vertical component of the absolute vorticity is the most important component for large-scale atmospheric flow, and that the large-scale structure of a two-dimensional non-divergent barotropic flow can be modeled by assuming that is conserved.
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 ...
The barotropic vorticity equation assumes the atmosphere is nearly barotropic, which means that the direction and speed of the geostrophic wind are independent of height. In other words, there is no vertical wind shear of the geostrophic wind. It also implies that thickness contours (a proxy for temperature) are parallel to upper level height ...
An inward, radial flow, tends to concentrate vorticity in a narrow column around the symmetry axis, while an axial stretching causes the vorticity to increase. At the same time, viscous diffusion tends to spread the vorticity. The stationary Burgers vortex arises when the three effects are in balance.
Crocco's theorem is an aerodynamic theorem relating the flow velocity, vorticity, and stagnation pressure (or entropy) of a potential flow.Crocco's theorem gives the relation between the thermodynamics and fluid kinematics.