Instability behavior of odd viscosity-induced viscous fluid over a vibrating bed

• Main Authors: Hossain, Md. Mouzakkir, Saha, Mrityunjoy, Behera, Harekrushna, Ghosh, Sukhendu
• Format: Journal Article
• Language: English
• Published: 30-09-2024
• Subjects: Physics - Fluid Dynamics
• DOI: 10.48550/arxiv.2409.20482

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.