# 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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We aim to derive a (2+ 1)-dimensional variable coefficient KdV (3D VCKdV) equation from the barotropic and quasi-geostrophic potential vorticity equation without dissipation on a beta-plane.
Momentum equation can be written into vorticity equation in the following form:
While, as we know, the (2 + l)-dimensional model can be applied to reflect the evolution of envelope Rossby solitary waves in a plane, which is more suitable for the real ocean and atmosphere, in this paper, by using the method of multiple scales and perturbation method, starting from the barotropic atmospheric vorticity equation, we will derive the coupled (2 + 1)-dimensional nonlinear Schrodinger equations for envelope Rossby solitary waves in Section 2.
Under some assumptions the Rossby wave dynamics at the so-called equivalent-barotropic level of the atmosphere can be described by the following vorticity equation [52, 53]:
Courtier, "Variational assimilation of meteorological observations with the adjoint vorticity equation. I: theory," Quarterly Journal of the Royal Meteorological Society, vol.
Interestingly Navier-Stokes equation which implies vorticity equation can also be rewritten in terms of Yukawa equation ;
Vertically oriented vortex tubes motion can be expressed by the vorticity equation in the z-direction  as d[zeta]/dt = [zeta] x [partial derivative]w/[partial derivative]x + [eta] x [partial derivative]w/[partial derivative]y + [zeta] x [partial derivative]w/[partial derivative]z, (1) where ([xi], [eta], [zeta]) are vorticities in the (x, y, z) directions, respectively, and w is the z-component of velocity.
Rossby waves are large-scale atmospheric movement and satisfy the dimensionless quasigeostrophic potential vorticity equation as follows [17, 18]:
Carey, "High-order compact scheme for the steady stream-function vorticity equations," International Journal for Numerical Methods in Engineering, vol.
Another basis can be developed by considering the momentum, continuity, and vorticity equations. For steady, incompressible, low-Reynolds-number flow in a passage having nearly parallel walls, the Navier-Stokes equations become

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