Propagation of perturbations and meandering in a free surface shallow water jet

Abstract

A shallow water free-surface turbulent jet is investigated at Froude numbers variable between about 0.15 and 0.6 and a Reynolds number equal to 5000, with a jet height-to-width aspect ratio variable from 0.5 to 1.1. In these experimental conditions, the flow is unstable and develops local transverse instabilities, which are amplified to a global meandering motion, forcing the jet to oscillate orthogonally to its axis. Instantaneous and averaged velocity fields are obtained by means of high-density, correlation-based time-resolved Particle Tracking Velocimetry. From the average point of view, the present jet configuration resembles a confined jet condition similar to that of wall jets, but with additional relevant three-dimensional effects, retaining self-similar properties, with a net co-flow and some ambient fluid entrainment. For increasing Froude numbers, such configuration is moved downstream and the jet spreading is delayed. The high resolution in space and time of present measurements allows to locally detect and following perturbed patterns and to derive amplitude and frequency of oscillation of the global meandering motion, the former increasing with axial distance and decreasing with Froude number, the latter doing just the opposite. The velocity of propagation of perturbed patterns is also investigated in comparison to the jet mean velocity, the local celerity of propagation of fluctuating velocity fields being derived. Results indicate that axial fluctuations propagate downstream similarly to transverse fluctuations along the orthogonal direction, thus showing a close coupling among the two motions and the onset of a self-sustained mechanism driven by the mean flow, responsible for the generation of the macroscopic meandering motion. This effect is in agreement with numerical predictions and is emphasised as the Froude number increases.