The decay of axisymmetric homogeneous turbulence

The decay of a homogeneous turbulence generated by an axisymmetric distribution of random impulsive forces acting at the initial instant is considered. The impulsive forces may be either parallel or perpendicular to the symmetry axis. For impulsive forces which result in a kappa(exp 4) low wavenumber energy spectrum of the turbulence, it is determined that the flow approaches isotropy on all scales of motion at long-times provided the Reynolds number is large. However, for the type of impulsive forces originally proposed by Saffman in which a sq kappa low wavenumber energy spectrum is produced, the turbulence approaches isotropy only at the smallest scales and remains significantly anisotropic at the largest and energy-containing scales. Nevertheless, a similarity state of the flow field establishes itself asymptotically, in which the kinetic energy per unit mass of the turbulence decays as t(exp -6/5)