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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:
The absolute vorticity is computed from the air velocity relative to an inertial frame, and therefore includes a term due to the Earth's rotation, the Coriolis parameter. The potential vorticity is absolute vorticity divided by the vertical spacing between levels of constant (potential) temperature (or entropy ).
Relative volatility is a measure comparing the vapor pressures of the components in a liquid mixture of chemicals. This quantity is widely used in designing large industrial distillation processes. [ 1 ] [ 2 ] [ 3 ] In effect, it indicates the ease or difficulty of using distillation to separate the more volatile components from the less ...
where is the relative vorticity, is the layer depth, and is the Coriolis parameter. The conserved quantity, in parenthesis in equation (3), was later named the shallow water potential vorticity. For an atmosphere with multiple layers, with each layer having constant potential temperature, the above equation takes the form
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 ...
Circulation can be related to curl of a vector field V and, more specifically, to vorticity if the field is a fluid velocity field, =.. By Stokes' theorem, the flux of curl or vorticity vectors through a surface S is equal to the circulation around its perimeter, [4] = = =
Here is the relative vorticity, the horizontal wind velocity vector, whose components in the and directions are and respectively, the absolute vorticity +, is the Coriolis parameter, = the material derivative of pressure , ^ is the unit vertical vector, is the isobaric Del (grad) operator, () is the vertical advection of vorticity and ...
In fluid mechanics, the Okubo–Weiss parameter, (normally given by "W") is a measure of the relative importance of deformation and rotation at a given point. It is calculated as the sum of the squares of normal and shear strain minus the relative vorticity.