How Bottom Friction Reshapes Vortices in Shallow Water express
Water in a puddle after rain swirls differently than in a deep lake. A thin layer of fluid feels the bottom, and that changes the nature of its vortices. Scientists created such a layer in the lab: they poured in an electrolyte, ran a current and a magnetic field, and the fluid began to move. Then, using cameras and tiny particles, they tracked the motion down to the smallest swirls, just a fraction of a millimeter across.
Away from the bottom, vortices turned out to be the same in all directions, like snowflakes in a perfect pattern. But right at the bottom, the picture breaks: friction slows motion along the flow, while across it, it barely interferes. This difference, like a crack in glass, creeps from small vortices to large ones. Energy flows from small swirls to big ones, and the big ones gradually lose their symmetry.
This transfer of asymmetry matters for weather forecasts and ocean currents. After all, the atmosphere and the ocean are also thin layers on the planet's surface, and friction with the ground or seabed affects large vortices such as cyclones. Understanding this mechanism helps improve climate models and predictions of water movement in narrow straits.
Original abstract
as written by the authors arXiv:2601.01258
We experimentally investigate quasi-two-dimensional (Q2D) forced shallow flows in the presence of solid boundaries and analyze the deviation from the Kolmogorov-Kraichnan (KK) theory. Complex motion is generated using a thin electrolyte subject to electromagnetic forces, and we employ particle tracking velocimetry to resolve the flow properties down to the Kolmogorov scale. Although the velocity probability distribution function closely resembles a Gaussian, deviations from Gaussianity emerge for velocity increments as scales decrease. The second-order structure function supports the onset of local anisotropy at small scales. The sign of the third-order structure function indicates the dominance of the inverse cascade in energy transfer, and the cross-correlation between longitudinal and transverse directions proves to be significant at large scales. The breakdown of local isotropy is consistent with the effect of bottom friction, which primarily affects the longitudinal motion, while leaving the perpendicular direction unaffected. This local anisotropy propagates to larger scales via the inverse energy cascade, with nonlinear interactions eventually influencing the perpendicular direction.
In the experiment, the vortices were smaller than a millimeter, and their speed changed within fractions of a second. To capture this, cameras shot thousands of frames per second.