发表机构
Northeast Forestry University; The Hong Kong Polytechnic University（东北林业大学; 香港理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究探究湍流级串方向所需信息，通过Haar相位保留二次量，发现非线性Navier-Stokes动力学能恢复有符号通量，而线性或冻结控制不能，表明级串箭头需额外信息。
AI 中文摘要
哪些信息告诉湍流以何种方向级串？我们应用Haar分布的Hermitian相位，这些相位保留指定的同模态二次信息，包括模态振幅、能谱和同模态两点时间关联。对于相位-Haar系综，任何可积的奇通量泛函的期望值为零。有限系综强烈抑制主区块中的平均传递和前向事件偏差。一个独立区块保留符号分离，但未能通过尺度-8平均准则。在匹配的演化协议中，非线性Navier-Stokes动力学将选定的有符号通量标量恢复到接近其自然参考值，而线性演化和振幅匹配的冻结控制则不能。通量与局部三次几何标量一同恢复，但高局部关联可能在箭头被擦除后仍存活。因此，有符号传递需要超出所保留二次记录的信息；所测试的非线性动力学重建了它。
英文摘要
Which information tells a turbulent flow which way to cascade? We apply Haar-distributed Hermitian phases that retain prescribed same-mode quadratic information, including modal amplitudes, the energy spectrum, and same-mode two-time correlations. For the phase-Haar ensemble, the expectation of any integrable odd flux functional is zero. Finite ensembles strongly suppress mean transfer and forward-event bias in the primary block. An independent block retains sign separation but fails the scale-8 mean criterion. In matched evolution protocols, nonlinear Navier-Stokes dynamics restores the selected signed-flux scalar close to its natural reference, whereas linear evolution and an amplitude-matched frozen control do not. Flux and a local cubic geometry scalar recover together, yet high local correlation can survive erasure of the arrow. Signed transfer thus requires information beyond the retained quadratic record; the tested nonlinear dynamics rebuilds it.
Comments17 pages, 10 figures; includes Supplemental Material. Code and processed records: https://github.com/zhaoyang7719286-hub/turbulent-cascade-arrow
