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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:
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 ...
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 ).
This relative movement generates fluid friction, which is a factor in developing turbulent flow. Counteracting this effect is the viscosity of the fluid, which tends to inhibit turbulence. The Reynolds number quantifies the relative importance of these two types of forces for given flow conditions and is a guide to when turbulent flow will ...
The number of vortices used vary with the required pressure distribution resolution, and with required accuracy in the computed aerodynamic coefficients. A typical number of vortices would be around 100 for an entire aircraft wing; an Aeronautical Research Council report by Falkner published in 1949 mentions the use of an "84-vortex lattice ...
However, a linear theory cannot be extended much beyond the initial state. If nonlinear interactions are taken into account, asymptotic analysis suggests that for large and finite <, where is a critical value, the Fourier coefficient decays exponentially. The vortex sheet solution is expected to lose analyticity at the critical time.
The two-dimensional stream function is based on the following assumptions: The flow field can be described as two-dimensional plane flow, with velocity vector
where is the relative vorticity, is the layer depth, and is the Coriolis parameter. The conserved quantity, in parentheses 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