振动床面上奇数粘性诱导的粘性流体的不稳定性行为
Instability behavior of odd viscosity-induced viscous fluid over a vibrating bed
AI总结：
本文通过理论稳定性分析研究了奇数粘性对振动倾斜床面上粘性流体不稳定性的影响，识别了重力、次谐波、谐波及剪切不稳定性，并揭示了奇数粘性对各类型不稳定性的稳定或抑制作用。
摘要：
本文致力于对振动倾斜刚性床面上的粘性液体进行理论稳定性分析，此时流体受到奇数粘性的影响。这种影响是由于时间反演对称性破缺而在经典流体中出现的。刚性底面沿流向和横流方向振动。利用正则模态方法得到时间相关的Orr-Sommerfeld特征值问题，并基于Chebyshev配点法和Floquet理论进行求解。识别了奇数粘性系数对不同类型不稳定性的影响，包括重力不稳定性、次谐波不稳定性和谐波不稳定性。重力不稳定性出现在长波区域，而共振波不稳定性出现在有限波数区域。重力不稳定性是由于重力驱动力在流体流动中产生的，次谐波不稳定性出现在较低的强迫振幅下，而谐波不稳定性出现在相对较高的强迫振幅下。研究发现，当强迫振幅超过其临界值时，次谐波共振和谐波共振就会出现。较高的奇数粘性有助于稳定重力不稳定性，而较大的奇数粘性会减弱次谐波共振以及在高强迫振幅下激发的谐波共振。此外，当雷诺数足够高且倾角较小时，在有限波数范围内会出现一种新的不稳定性，称为剪切不稳定性，它与上述三种不稳定性同时出现，并且当时间反演对称性破缺时，这种不稳定性会变弱。
英文摘要：
The manuscript focuses on the theoretical stability analysis of the viscous liquid over a vibrating inclined rigid bed when the fluid undergoes an impact of odd viscosity. Such an impact emerges in the classical fluid owing to the broken time-reversal symmetry. The rigid bottom vibrates in streamwise and cross-stream directions. The time-dependent Orr-Sommerfeld eigenvalue problem is obtained using the normal mode approach and resolved based on the Chebyshev-collocation method and the Floquet theory. The effect of the odd viscosity coefficient on the different types of instability gravitational, subharmonic, and harmonic are identified. The gravitational instability arises in the longwave region, whereas the resonated wave instability appears in the finite wavenumber region. The gravitational instability is generated in the fluid flow owing to the gravity driving force, whereas the subharmonic instability appears for lower forcing amplitude and the harmonic instability emerges for comparatively higher forcing amplitude. It is found that the subharmonic and harmonic resonances appear when the forcing amplitude surpasses its critical value. A higher odd viscosity leads to stabilizing the gravitational instability, whereas a larger odd viscosity diminishes the subharmonic resonance along with the harmonic resonance instigated at a high forcing amplitude. Further, a new instability, named shear instability in the finite wavenumber range emerges together with the aforementioned three instabilities when the Reynolds number is sufficiently high with a low angle of inclination and becomes weaker when the time-reversal symmetry breaks.
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