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 η_L. The Liutex spectrum is E_L (k) ∼ C[n(A)^1/2η_L]^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 Liutex_p (l) ≡ 〈[δR_∥(l)]^p〉 which are in dependent of scales. It is found that Liutex_p (l) ∼ C′(η_L)^p/3l⁰ by dimensional analysis.

本文对流道湍流中的 Liutex 相似性进行了扩展和修正。Liutex 相似性没有粘性耗散，放松了 K41 的非常高的雷诺数假设。首次提出并估计了二维通道湍流中的 Liutex 相似性假设，这表明 Liutex 场的统计特性唯一且普遍地由尺度l、每个区域A 的Liutex 涡数密度n ( A )和平均耗散率决定Liutex 震级η _L的平方。Liutex 谱为E _L ( k ) ∼ C [ n ( A ) ^1/2η _L ] ^1/3 k ^-5/3在能谱表现出双级联的惯性范围内。二维中 Liutex 谱的标度行为与雷诺数无关。Liutex 结构函数被定义为 Liutex _p ( l ) ≡ 〈[ δR _∥ ( l )] ^p〉，它们与尺度有关。通过量纲分析发现，Litex _p ( l ) ∼ C ′( η _L ) ^{p /3} l ⁰。