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In fluid dynamics, the Taylor–Green vortex is an unsteady flow of a decaying vortex, which has an exact closed form solution of the incompressible Navier–Stokes equations in Cartesian coordinates. It is named after the British physicist and mathematician Geoffrey Ingram Taylor and his collaborator A. E. Green.
Contents
Original work
In the original work of Taylor and Green, a particular flow is analyzed in three spatial dimensions, with the three velocity components
The continuity equation
An exact solution in two spatial dimensions is known, and is presented below.
Incompressible Navier–Stokes equations
The incompressible Navier–Stokes equations in the absence of body force, and in two spatial dimensions, are given by
The first of the above equation represents the continuity equation and the other two represent the momentum equations.
Taylor–Green vortex solution
In the domain
where
The pressure field
The stream function of the Taylor–Green vortex solution, i.e. which satisfies
Similarly, the vorticity, which satisfies
The Taylor–Green vortex solution may be used for testing and validation of temporal accuracy of Navier–Stokes algorithms.