Vortex imprints on a free surface as proxy for surface divergence

In turbulence near a free surface, strong vortices attach to the surface, creating surface imprints visible as nearly circular 'dimples'. By studying these imprints in direct numerical simulation (DNS) data we make two observations. First, the imprints of surface-attached vortices can be very effectively distinguished from other turbulent surface features using two physical features: they are nearly circular in shape, and persist for a long time compared with other pertinent time scales. Secondly, the instantaneous number of surface dimples from surface-attached vortices in an area, N(t), is intimately related to its mean-square surface divergence, beta(2)(t). We develop a simple and physically transparent computer vision procedure which, using the properties of low eccentricity and longevity, detects and tracks vortices from their surface features only, with sensitivity and accuracy of 90% or better. We compare N(t) and beta(2)(t), finding a normalised cross-correlation of 0.90, with changes in N lagging around 0.8T(infinity) behind those in beta(2) (T-infinity is an integral time scale), confirming the common observation that vortices are spawned by strong upwelling events where beta(2) is large. These findings suggest that the rate of mass flux across the surface, being closely related to surface divergence, can be estimated remotely in some natural flows using visible free-surface dimples as proxy.

Automated summary

Through the study of direct numerical simulation (DNS) data, it is found that the imprints of surface-attached vortices can be effectively distinguished from other turbulent surface features based on their circular shape and longer persistence. A computer vision procedure is developed to detect and track vortices solely based on their surface features, with a sensitivity and accuracy of 90% or better. The relationship between the number of surface dimples and the mean-square surface divergence suggests that visible free-surface dimples can be used as a proxy to remotely estimate the rate of mass flux across the surface in some natural flows.