G. I. Taylor gave the solution for a special case where , where  is a constant in 1923.  He showed that the separation  satisfies the equation and also
Taylor also considered an example, a decaying system of eddies rotating alternatively in opposite directions and arranged in a rectangular array
which satisfies the above equation with , where  is the length of the square formed by an eddy. Therefore, this system of eddies decays as
O. Walsh generalized Taylors eddy solution in 1992. Walshs solution is of the form , where  and