Viscous Bending Mitigates the Spontaneous Meandering of Rivulets in Hele-Shaw Cells
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| Format: | Preprint |
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2026
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| _version_ | 1866914458450788352 |
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| author | Lay, Grégoire Le Daerr, Adrian |
| author_facet | Lay, Grégoire Le Daerr, Adrian |
| contents | We investigate the spontaneous meandering of slender rivulets in Hele-Shaw cells and identify the physical mechanism that selects the most unstable wavenumber, a quantity that has remained elusive even since the identification of the instability threshold [Daerr et al., Phys. Rev. Lett. 106, 184501 (2011)]. Earlier criteria did not distinguish between wavelengths and thus predicted an undiscriminated amplification of arbitrarily short perturbations. By incorporating viscous bending into the depth-averaged Navier-Stokes equations, we show that this effect is responsible for the selection of a fastest-growing mode, answering a question that has remained open for 15 years. We answer the open question of whether the meandering instability is absolute or convective. Our analysis also provides a simpler alternative derivation of the instability criterion, based on a low-viscosity assumption, and finally it yields a new physical interpretation of the mechanism: the destabilization arises directly from friction effects, instead of being caused by inertial forces. Together, these results complete the linear-stability picture of rivulet meandering in confined geometries, and establish viscous bending as a key parameter governing wavelength selection. They lay the groundwork for future exploration of the nonlinear features of the spontaneous meandering instability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_07222 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Viscous Bending Mitigates the Spontaneous Meandering of Rivulets in Hele-Shaw Cells Lay, Grégoire Le Daerr, Adrian Fluid Dynamics Soft Condensed Matter We investigate the spontaneous meandering of slender rivulets in Hele-Shaw cells and identify the physical mechanism that selects the most unstable wavenumber, a quantity that has remained elusive even since the identification of the instability threshold [Daerr et al., Phys. Rev. Lett. 106, 184501 (2011)]. Earlier criteria did not distinguish between wavelengths and thus predicted an undiscriminated amplification of arbitrarily short perturbations. By incorporating viscous bending into the depth-averaged Navier-Stokes equations, we show that this effect is responsible for the selection of a fastest-growing mode, answering a question that has remained open for 15 years. We answer the open question of whether the meandering instability is absolute or convective. Our analysis also provides a simpler alternative derivation of the instability criterion, based on a low-viscosity assumption, and finally it yields a new physical interpretation of the mechanism: the destabilization arises directly from friction effects, instead of being caused by inertial forces. Together, these results complete the linear-stability picture of rivulet meandering in confined geometries, and establish viscous bending as a key parameter governing wavelength selection. They lay the groundwork for future exploration of the nonlinear features of the spontaneous meandering instability. |
| title | Viscous Bending Mitigates the Spontaneous Meandering of Rivulets in Hele-Shaw Cells |
| topic | Fluid Dynamics Soft Condensed Matter |
| url | https://arxiv.org/abs/2604.07222 |