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. Kerr–Dold vortices in axisymmetric stagnation point flows was described by P. Rajamanickam. 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 first observed experimentally in a four-roll mill apparatus by Lagnado and L. Gary Leal. and in a crossed rectangular channel by V. N. Kalashnikov and M. G. Tsiklauri.
Mathematical description The stagnation point flow, which is already an exact solution of the Navier–Stokes equation is given by U = ( 0 , − A y , A z ) {\displaystyle \mathbf {U} =(0,-Ay,Az)} , where A {\displaystyle A} is the strain rate. To this flow, an additional periodic disturbance can be added such that the new velocity field can be written as
u = [ 0 − A y A z ] + [ u ( x , y ) v ( x , y ) 0 ] {\displaystyle \mathbf {u} ={\begin{bmatrix}0\\-Ay\\Az\end{bmatrix}}+{\begin{bmatrix}u(x,y)\\v(x,y)\\0\end{bmatrix}}}
where the disturbance u ( x , y ) {\displaystyle u(x,y)} and v ( x , y ) {\displaystyle v(x,y)} are assumed to be periodic in the x {\displaystyle x} direction with a fundamental wavenumber k {\displaystyle k} . Kerr and Dold showed that such disturbances exist with finite amplitude, thus making the solution an exact to Navier–Stokes equations. Introducing a stream function ψ {\displaystyle \psi } for the disturbance velocity components, the equations for disturbances in vorticity-streamfunction formulation can be shown to reduce to
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