# vorticity equation

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## vorticity equation

[vȯr′tis·əd·ē i‚kwā·zhən]
(fluid mechanics)
An equation of fluid mechanics describing horizontal circulation in the motion of particles around a vertical axis: (d / dt) (S + f) = - (S + f) divh c, where (S + f) is the absolute vorticity (S is the relative vorticity and f is the Coriolis parameter) and divh c is the horizontal divergence of the fluid velocity.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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The convective term in the vorticity transport equation is integrated over the control volume [A.sub.C.V.].
Assembly of the vorticity transport equation at each node i yields
The stochastic vorticity transport equation should be handled carefully as we have the velocities ([u.sub.j], [v.sub.j]), and the vorticity gradients ([partial derivative][[omega].sub.i]/[partial derivative]x, [partial derivative][[omega].sub.i][partial derivative]y) are from different stochastic levels (levels j and i).
In the vorticity-stream function formulation, only the vorticity transport equation has these expensive storage and computational costs.
Vorticity transport equation. This computational scheme involves the forward-time, center-space (FTCS) method.
The vorticity transport equation will be obtained by taking curl of momentum equation (2) and using mass conservation (1).
Numerical method for vorticity transport equation. The rectangular grid system used here is schematically illustrated in Fig.
The equations that govern the incompressible laminar flow are the vorticity transport equation,
In the numerical method, the vorticity transport equation is first solved and then the pressure distribution equation is solved without any assumptions made for pressure distribution.

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