An Extended Similarity in Channel Turbulence

In this paper, Liutex similarity is extended and revised in channel turbulence. Liutex similarity is free from viscous dissipation, relaxing the very high Reynolds number assumption of K41. Liutex similarity hypothesis in 2-D channel turbulence is first proposed and estimated, which denotes that the statistical properties of Liutex field are uniquely and universally determined by the scale l, Liutex vortex number density n(A) with each area A and mean dissipation rate of square of Liutex magnitude ηL. The Liutex spectrum is EL (k) ∼ C[n(A)1/2ηL]1/3k−5/3 in the inertial range where energy spectrum exhibits double cascades. The scaling behaviors of Liutex spectrum in 2-D are independent of Reynolds number. Liutex structure functions are defined as Liutexp (l) ≡ 〈[δR∥(l)]p〉 which are in dependent of scales. It is found that Liutexp (l) ∼ C′(ηL)p/3l0 by dimensional analysis.