An inequality concerning the production of vorticity in isotropic turbulence

An inequality is demonstrated involving the rate of production S of mean-square vorticity in isotropic turbulence and a factor γ which may be said to allow for intermittency or for the non-vanishing of fourth-order cumulants. An extreme state, corresponding to equality of this relationship, occurs if S = 0·64 and γ = 2·14. The experimental values are S = 0·4 and γ = 4. Another kinematical relation shows that the mechanism of vorticity production resembles collision between fluid particles rather than the swirling of contracting jets.