AI 中文总结
研究宽通道库埃特湍流解析基础不明问题，利用二阶统计状态动力学，发现其定点状态源于模态RSS不稳定性，在展向波数3时平衡，由特定结构构成涨落协方差，湍流通过定点RSS晶胞展向平铺产生。
AI 中文摘要
宽通道库埃特（WCC）湍流主要由通过自维持过程维持的稳定滚动条纹结构（RSS）组成，但速度变量中的纳维 - 斯托克斯方程不存在线性RSS不稳定性或稳定平衡，使得WCC湍流状态的解析基础模糊不清。我们表明，在二阶统计状态动力学（SSD）中，库埃特湍流的定点状态源于模态RSS不稳定性，并在展向波数为3时作为精确的吸引性RSS达到平衡。该定点包括一个一阶流向平均流和一对共轭中性本征模，通过滚动平流而非粘性进行正则化，形成一个二阶涨落协方差。WCC湍流通过此定点RSS晶胞的展向平铺产生。
英文摘要
Wide-channel Couette (WCC) turbulence consists primarily of quasi-steady roll-streak structures (RSS) maintained by a self-sustaining process (SSP), yet the Navier-Stokes equations in velocity variables admit no linear RSS instability or stable equilibrium, leaving the WCC turbulent state's analytic basis obscure. We show that, in the statistical state dynamics (SSD) of a second-order closure of the Navier-Stokes equations, Couette turbulence arises from a modal RSS instability and equilibrates as a stable fixed point at spanwise wavenumber 3. This fixed point comprises a streamwise-mean flow and a pair of counterpropagating neutral eigenmodes, regularized by roll advection rather than viscosity. This stable equilibrium identifies both a canonical turbulence solution and its self-sustaining process (SSP), and characterizes their analytic structure. WCC turbulence arises as a spanwise tiling by this stable fixed-point RSS unit cell. Predictions of this SSD theory are corroborated by comparison with direct numerical simulation.
Comments8 pages, 6 figures, submitted to PRFluids
