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Updated: Jun 1, 2026
06:42
Magnetically Induced Rotating Rayleigh-Taylor Instability
Published on: March 3, 2017
Inertial effects on rotating Hele-Shaw flows.
Eduardo O Dias1, José A Miranda
1Departamento de Física, Universidade Federal de Pernambuco, Recife, Pernambuco 50670-901, Brazil.
Summary
Inertial effects stabilize viscous fingering patterns in rotating Hele-Shaw cells. While inertia narrows finger tips, it does not change the number of fingers or the unstable mode bandwidth.
Area of Science:
- Fluid Dynamics
- Pattern Formation
- Hele-Shaw Flow
Background:
- Viscous fingering in Hele-Shaw cells is a classic problem in fluid dynamics.
- Understanding pattern formation under rotation and inertial effects is crucial for various applications.
- Surface tension plays a significant role in stabilizing fluid interfaces.
Purpose of the Study:
- To investigate the impact of inertial effects on radial viscous fingering in a rotating Hele-Shaw cell.
- To analyze how inertia influences the stability and morphology of emergent fingering patterns.
- To characterize the role of rotational Reynolds number in governing inertial forces.
Main Methods:
- Utilized a modified Darcy's law derived from gap-averaged Navier-Stokes equations, including inertial terms.
- Employed a mode coupling approach for analytical description of linear and weakly nonlinear dynamics.
- Analyzed the influence of the rotational Reynolds number on flow behavior.
Main Results:
- Linear stability analysis revealed a stabilizing role for inertia.
- Inertia did not alter the characteristic number of fingers or the width of unstable modes.
- Weakly nonlinear analysis showed inertia favoring narrower finger tips and restraining length variability.
Conclusions:
- Inertial effects play a stabilizing role in radial viscous fingering.
- While inertia influences finger morphology (narrower tips), it does not change the overall number of fingers.
- Inertial effects modulate finger competition, leading to more uniform finger lengths.
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