In fluid dynamics, Kerr–Dold vortex is an exact solution of Navier–Stokes equations, which represents steady periodic vortices superposed on the stagnation point flow (or extensional flow).
The solution was discovered by Oliver S. Kerr and John W. Dold in 1994.
[1][2] These steady solutions exist as a result of a balance between vortex stretching by the extensional flow and viscous diffusion, which are similar to Burgers vortex.
These vortices were observed experimentally in a four-roll mill apparatus by Lagnado and L. Gary Leal.
[3] The stagnation point flow, which is already an exact solution of the Navier–Stokes equation is given by
To this flow, an additional periodic disturbance can be added such that the new velocity field can be written as where the disturbance
direction with a fundamental wavenumber
Kerr and Dold showed that such disturbances exist with finite amplitude, thus making the solution an exact to Navier–Stokes equations.
for the disturbance velocity components, the equations for disturbances in vorticity-streamfunction formulation can be shown to reduce to where
A single parameter can be obtained upon non-dimensionalization, which measures the strength of the converging flow to viscous dissipation.
Since the expected vortex structure has the symmetry
Upon substitution, an infinite sequence of differential equation will be obtained which are coupled non-linearly.
To derive the following equations, Cauchy product rule will be used.
It can be shown that non-trivial solution exist only when
On solving this equation numerically, it is verified that keeping first 7 to 8 terms suffice to produce accurate results.
was already discovered by Craik and Criminale in 1986.