Taylor–Green vortex

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.

In the original work of Taylor and Green, a particular flow is analyzed in three spatial dimensions, with the three velocity components ${\displaystyle \mathbf {v} =(u,v,w)}$ at time ${\displaystyle t=0}$ specified by

The continuity equation ${\displaystyle \nabla \cdot \mathbf {v} =0}$ determines that ${\displaystyle Aa+Bb+Cc=0}$. The small time behavior of the flow is then found through simplification of the incompressible Navier–Stokes equations using the initial flow to give a step-by-step solution as time progresses.

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