On the decay of vortices in a second grade fluid

It is shown that the results established by Taylor (1923) for the linearly viscous fluid are unconditionally true, irrespective of the time scale which characterizes the fluid or the size of the vortices in the case of incompressible second grade fluids provided they are thermodynamically compatible. Taylor's findings were that the flow representing a double array of vortices which has the same periodicity in both the x and y directions is a solution to the equations of motion in two dimensions of a linearly viscous fluid. The relationship between the ratio of decay of the vortices and the periodicity of the vortices is investigated. It is found that if the periodicity is increased in the x or y directions, the vortices decay faster, and that they decay faster as the coefficient of viscosity increases.