AI 中文总结
研究高施密特数下分层交换流中界面霍尔姆博厄波起始的侧壁效应，用长管道、锐界面渐近理论确定受限调整弗劳德数\(Fr^*\)，通过线性稳定性分析等方法，表明\(Fr^*\)近似恒定临界值可准确预测波起始，调和差异并确立横向受限的控制作用。
AI 中文摘要
预测界面不稳定性的起始对于理解自然和工程分层剪切流中的湍流混合至关重要。本文研究了沿斜坡受限交换流中行进的霍尔姆博厄波的起始。早期分层倾斜管道实验已描绘了这种转变，基于测量或规定剖面的稳定性分析解释了它们的出现。然而，仍缺乏将强迫、几何形状、基流和波起始联系起来的预测准则。我们用三维层流交换流的长管道、锐界面渐近理论填补了这一空白，该理论包括侧壁摩擦的影响。所得解析解自然地确定了一个受限调整弗劳德数\(Fr^*\)，它将强迫和受限的影响统一为有效层流交换流的单一度量。利用该解在实际宽度平均模型中参数化侧壁阻力，我们在高施密特数下进行了线性稳定性分析和数值模拟。线性稳定性分析、直接数值模拟以及一系列管道宽度的现有实验共同表明，波起始可由\(Fr^*\)的近似恒定临界值准确预测。仅在非常窄的管道中出现偏差，其中侧壁不仅通过改变层流交换流影响不稳定性，还通过直接阻尼扰动和延迟波起始来影响。这些发现为波起始提供了预测准则，调和了实验配置之间长期存在的差异，并确立了横向受限作为分层剪切流中从层流交换到波驱动混合转变的基本控制因素。
英文摘要
Predicting the onset of interfacial instabilities is central to understanding turbulent mixing in natural and engineered stratified shear flows. Here, we study the onset of travelling Holmboe waves in confined exchange flows along a slope. Earlier stratified inclined duct experiments have mapped this transition, and stability analyses based on measured or prescribed profiles have explained their emergence. However, a predictive criterion linking forcing, geometry, base flow, and wave onset was still lacking. We closed this gap with a long-duct, sharp-interface asymptotic theory for the three-dimensional laminar exchange flow, including the effects of sidewall friction. The resulting analytical solution naturally identifies a confinement-adjusted Froude number, $Fr^*$, which unifies the effects of forcing and confinement into a single measure of the effective laminar exchange flow. Using this solution to parameterise sidewall drag in a practical width-averaged model, we perform linear stability analyses and numerical simulations at high Schmidt number. Together, linear stability analysis, direct numerical simulations, and existing experiments across a range of duct widths show that wave onset is accurately predicted by an approximately constant critical value of $Fr^*$. Deviations arise only in very narrow ducts, where sidewalls influence instability not only by modifying the laminar exchange flow but also by directly damping perturbations and delaying wave onset. These findings provide a predictive criterion for wave onset, reconcile long-standing discrepancies among experimental configurations, and establish lateral confinement as a fundamental control on the transition from laminar exchange to wave-driven mixing in stratified shear flows.
