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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 ...
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 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.
The absolute vorticity composes the planetary vorticity and the relative vorticity , reflecting the Earth’s rotation and the parcel’s rotation with respect to the Earth, respectively. The conservation of absolute vorticity η {\displaystyle \eta } determines a southward gradient of ζ {\displaystyle \zeta } , as denoted by the red shadow in c .
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 relative vorticity is the vorticity relative to the Earth induced by the air velocity field. This air velocity field is often modeled as a two-dimensional flow parallel to the ground, so that the relative vorticity vector is generally scalar rotation quantity perpendicular to the ground.
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 ...