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They note that the rate of change of mean-square vorticity in isotropic turbulence is proportional to the mean-cube of vorticity, which in turn is related to the skewness factor of the velocity derivative.
of change of mean-square vorticity is apparently proportional to (?
This term taken alone would lead to a blow-up of mean-square vorticity within a fi- nite time.
(The statement that the "viscous contribution is always the greater" clearly does not apply to the initial development of a field of turbulence concentrated at low wave-numbers in wave-number space; for such a field, the nonlinear contri- bution dominates and leads to initial rapid growth of mean-square vorticity, just as in the model problem treated by Taylor & Green 1937, now familiarly known as the 'Taylor-Green vortex'.)
There is still to this day great interest in the question as to whether, for an inviscid fluid, the mean-square vorticity (or indeed the pointwise distribution of vorticity) really can exhibit a singularity at finite time.
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