Shallow free-surface Stokes flow around a corner

Area of Science:

• Fluid dynamics
• Rheology
• Geophysics

Background:

• Investigating free-surface viscous flow on inclined planes is crucial for understanding natural phenomena like lava flows.
• The behavior of fluids spreading and detaching from channels with varying geometry presents complex challenges in fluid mechanics.

Purpose of the Study:

• To analytically, numerically, and experimentally investigate the steady lateral spreading of a free-surface viscous flow down an inclined plane.
• To model fluid motion using lubrication theory and determine the flow detachment point as a function of channel opening angle.
• To discuss implications for designing barriers to divert hazardous flows, such as lava flows.

Main Methods:

• Utilizing lubrication theory to model the viscous fluid flow.
• Employing analytical and numerical methods to compute the flow detachment distance.
• Conducting laboratory experiments to corroborate theoretical and numerical findings.

Main Results:

• The study accurately models the viscous flow detachment using lubrication theory.
• A similarity solution effectively describes the fluid motion far downslope after detachment.
• A simple expression provides a good approximation for the detachment point across various channel opening angles.

Conclusions:

• The developed model and findings offer a reliable method for predicting viscous flow detachment.
• The research provides valuable insights for the engineering of effective barriers for lava flow diversion.
• This work contributes to the fundamental understanding of free-surface viscous flows in expanding geometries.