Connecting the surface to the bottom through nonlinear effects

In remote regions of Canada, transportation authorities establish winter roads over frozen water bodies. Understanding deformation and strain in the ice requires accounting for the underlying bottom topography, where bumps and craters can generate waves that interact nonlinearly.

Ţugulan et al. computationally analyzed the nonlinear regime of floating ice over varying bottom topographies. They found that different flow regimes strongly influence ice sheet deformations, producing localized patterns at lower flow speeds and wake-like patterns when speeds increase. These results suggest bottom features can be arranged to influence the strain on the ice.

“A lot of existing methods like to analyze linear regimes,” said author Olga Trichtchenko. “We were able to use … all these computational techniques that weren’t maybe as available as they have been in recent years to actually resolve this complicated set of equations and really look at the nonlinear phenomena.”

The researchers began by rewriting the complex set of equations governing the physical interactions between the ice cover, water, and bottom topography as a reduced system centered on the ice-water interface. They discretized the equations and solved them using GPU-accelerated computations before comparing the results to predictions from linear theory.

The team found that increasing the size of the bumps or craters disproportionately increased wave size. In general, short flexural waves due to the presence of the ice preceded deformations, while longer gravity waves followed deformations.

Such computational explorations complement experiments and field measurements which can be too dangerous.

“This way, we can really do it quite fast and figure out regimes where it might be safer to cross one of these ice roads,” said Trichtchenko.

Source: “Three-dimensional steady nonlinear flexural-gravity waves over bottom topography,” by C. Ţugulan, O. Trichtchenko, and E. I. Părău, Physics of Fluids (2026). The article can be accessed at https://doi.org/10.1063/5.0340999 .