Abstract
Free-surface cusps appear as a generic feature in viscous flow with a free surface.
However, a mathematical description has so far only been possible by constructing exact solutions to the Stokes equation in very specific and idealized geometries, using complex mapping techniques. Here we use the boundary integral formulation of the Stokes equation to show that cusps are local singular solutions to Stokes’ equation. We recover Jeong and Moffatt’s [J. Fluid Mech. 241, 1 (1992)] local cusp solution in the limit of diverging cusp curvature, demonstrating its universality across all viscous flows.
However, a mathematical description has so far only been possible by constructing exact solutions to the Stokes equation in very specific and idealized geometries, using complex mapping techniques. Here we use the boundary integral formulation of the Stokes equation to show that cusps are local singular solutions to Stokes’ equation. We recover Jeong and Moffatt’s [J. Fluid Mech. 241, 1 (1992)] local cusp solution in the limit of diverging cusp curvature, demonstrating its universality across all viscous flows.
| Original language | English |
|---|---|
| Article number | 124001 |
| Number of pages | 21 |
| Journal | Physical Review Fluids |
| Volume | 8 |
| Issue number | 12 |
| DOIs | |
| Publication status | Published - 6 Dec 2023 |