发表机构
Bar-Ilan University; Karlsruhe Institute of Technology（巴伊兰大学; 卡尔斯鲁厄理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究推导了奇黏度推广的Orr--Sommerfeld--Squire方程，发现奇黏度可通过将剪切流瞬态增长转化为自持指数增长模式诱导新不稳定性，建立了瞬态增长、非正态性与非耗散力诱导不稳定性的联系。
AI 中文摘要
奇黏度是黏度张量的非耗散分量，产生于时间反演对称性破缺的流体中。尽管能守恒能量，我们证明奇黏度可通过产生常规流体中不存在的指数增长模式，定性改变流体动力学稳定性。针对平面泊肃叶流，我们推导了奇黏度推广的Orr--Sommerfeld--Squire方程，发现一种新的不稳定性，其首先在展向扰动中出现，再通过临界层内奇黏度力的放大扩展至斜向模式。该不稳定性源于剪切流的非正态动力学：常规流体通过升力机制支持瞬态增长的扰动，而奇黏度在法向速度与涡度间提供反馈，将这种瞬态增长转化为自持的指数增长模式。更普遍地，我们证明仅当未受扰系统支持瞬态增长时，守恒能量的扰动才能使非正态动力系统失稳。我们的结果建立了瞬态增长、非正态性与非耗散力诱导的不稳定性之间的直接联系，其意义超出奇黏度流体动力学范畴。
英文摘要
Odd viscosity is a nondissipative component of the viscosity tensor that arises in fluids with broken time-reversal symmetry. Despite conserving energy, we show that odd viscosity can qualitatively alter hydrodynamic stability by generating exponentially growing modes that are absent in conventional fluids. For plane Poiseuille flow, we derive the odd-viscous generalization of the Orr--Sommerfeld--Squire equations and find a new instability that first emerges for spanwise perturbations and extends to oblique modes through the amplification of odd-viscous forces in critical layers. The instability originates from the non-normal dynamics of shear flows: conventional fluids support transiently growing disturbances through the lift-up mechanism, while odd viscosity provides a feedback between wall-normal velocity and vorticity that converts this transient growth into a self-sustaining exponentially growing mode. More generally, we show that an energy-conserving perturbation can destabilize a non-normal dynamical system only when the unperturbed system supports transient growth. Our results establish a direct connection between transient growth, non-normality, and instability induced by nondissipative forces, with implications extending beyond odd-viscous hydrodynamics.
