Inertial range scaling of intense events in turbulence

The inertial range scaling exponents ζ(p) for the velocity difference moments 〈[u(x+r)-u(x)${]}^{\mathit{p}}$〉 in high Reynolds number turbulence are considered for large values of p. Two different models are considered. In the first the asymptotic behavior of ζ(p) is 1.440${\mathit{p}}^{1/2}$, and in the second it is (p/9). It is shown that these two models are indistinguishable experimentally for p<100, but that the underlying dynamical assumption about the most intense turbulent events in the two models is essentially different.