High-resolution direct numerical simulation data of a turbulent plane jet at Reynolds numbers italic Re Subscript upper H Baseline equals 10 Superscript 4 Re H = 10 4 ReH= 10⁴ and 10 Superscript 5 10 5 10⁵, based on the nozzle width, are employed to investigate the behaviour of the structure functions in the flow region with external intermittency. In the intermittent turbulent region, the conditional second-order longitudinal and transverse structure functions exhibit self-similar behaviour at small and intermediate scales. Moreover, as the order increases from the second to the sixth, the conditional higher even-order structure function profiles progressively deviate from self-similarity and the predictions of Kolmogorov’s universal equilibrium theory. The conditional third-order structure function only displays self-similarity within the small-scale dissipation range, albeit the range of self-similarity extends to progressively larger values of r divided by eta Superscript upper T r / η T r/ T for a higher Reynolds number, where eta Superscript upper T η T T denotes conditional Kolmogorov length scale and r r r is the separation distance. As the intermittency factor decreases, the unsteady term in the Kármán–Howarth equation becomes more significant, leading to a larger deviation from Kolmogorov’s 4 divided by 5 4 / 5 4/5 law. The extrapolation results based on the empirical formula for the structure function left angle bracket delta u Superscript prime n Baseline right angle bracket left parenthesis r right parenthesis ⟨ δ u ′ n ⟩ (</
Xie et al. (Fri,) studied this question.