On the local anisotropy of quasi-two-dimensional forced shallow flow: An experimental study

TL;DR

This experimental study investigates how local anisotropy develops in quasi-two-dimensional forced shallow flows, revealing deviations from classical turbulence theory due to boundary effects and inverse energy cascade dynamics.

Contribution

It provides new experimental evidence on the anisotropic behavior and energy transfer mechanisms in Q2D flows, highlighting the impact of bottom friction and nonlinear interactions.

Findings

Velocity distribution is Gaussian-like but shows deviations at small scales.

Local anisotropy emerges at small scales, influenced by bottom friction.

Inverse cascade dominates energy transfer, propagating anisotropy to larger scales.

Abstract

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.