Vortex structures under dimples and scars in turbulent free-surface flows

TL;DR

This study uses direct numerical simulations to link surface features like dimples and scars in turbulent free-surface flows to the underlying vortical structures, revealing distinct vortex signatures associated with each surface pattern.

Contribution

It provides a detailed analysis of the vortex structures beneath dimples and scars, establishing their different orientations and depth profiles in turbulent free-surface flows.

Findings

Vortex presence beneath dimples decreases with depth, influenced by dimple size and turbulence.

Vortex presence beneath scars peaks at the viscous layer edge, about a quarter of the Taylor microscale deep.

Dimples are linked to vertical vortices, scars to horizontal vortices.

Abstract

Turbulence beneath a free surface leaves characteristic long-lived signatures on the surface, such as upwelling 'boils', near-circular 'dimples' and elongated 'scars', easily identifiable by eye, e.g., in riverine flows. In this paper, we use Direct Numerical Simulations to explore the connection between these surface signatures and the underlying vortical structures. We investigate dimples, known to be imprints of surface-attached vortices, and scars, which have yet to be extensively studied, by analysing the conditional probabilities that a point beneath a signature is within a vortex core as well as the inclination angles of sub-signature vorticity. The analysis shows that the likelihood of vortex presence beneath a dimple decreases from the surface down through the viscous and blockage layers in a near-Gaussian manner, influenced by the dimple's size and the bulk turbulence. When expressed as a function of depth over the Taylor microscale $\lambda_T$, this probability is independent of Reynolds and Weber number. Conversely, the probability of finding a vortex beneath a scar increases sharply from the surface to a peak at the edge of the viscous layer, at a depth of approximately $\lambda_T/4$. Distributions of vortical orientation also show a clear pattern: a strong preference for vertical alignment below dimples and an equally strong preference for horizontal alignment below scars. Our findings suggest that scars can be defined as imprints of horizontal vortices approximately a quarter of the Taylor microscale beneath the surface, analogous to how dimples can be defined as imprints of surface-attached vertical vortex tubes.