Physics of
Fluids **7** (1995) pp. 600-605

### The decay of axisymmetric homogeneous turbulence

- J. R.
Chasnov
*The Hong Kong University of Science and Technology, Hong
Kong*

The decay of a homogeneous turbulence generated by an axisymmetric distribution of random impulsive forces acting at the initial
instant is studied by means of large-eddy simulations. The impulsive forces may be either parallel or perpendicular to the symmetry
axis. For impulsive forces which result in a k^{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 [* J. Fluid Mech* **27**, 581 (1967)], in which a k^{2} 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^{-6/5}.

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