Shallow-Water Plane and Tidal Jets

Abstract

This work uses field and laboratory measurements to improve the understanding of how shallow water depths affect the velocity and turbulence structure of fluid jets, in particular how a low aspect ratio (AR=depth/width) changes the structure of plane jets. The motivation for the work was the Otago Harbour (New Zealand) ebb tidal jet, a strong tidal jet 2 km long and 500 m wide with AR= 0.03. Tidal jets are globally common features and play an important role in the distribution of water-borne constituents within and in the vicinity of tidal inlets. Five vessel-mounted Acoustic Doppler Current Profiler (ADCP) surveys of the jet were combined and spatially and temporally interpolated using Radial Basis Functions (RBFs), an approach that was only recently adapted for ADCP data and has never before been used on such a large data set. The resulting velocity field agreed well with a previous study and showed the typical tidally developing jet and a large vortex to its Eastern side. The RBF method also allowed for the first direct extraction of the tidal jet’s dynamical terms, which revealed that during peak ebb flow the dynamical balance was dominated by the advection and pressure gradient terms, with bottom friction (BF), local acceleration and Coriolis contributing in certain areas. Here, a simplified model of an ebb jet, a laboratory plane jet, with much lower ARs (0.06 ≤AR≤ 0.15) than those of any previous laboratory plane jet studies (mostly AR≫ 1), is used to determine how bottom friction influences the plane jet. These low ARs were made possible due to a novel self-regulating lateral entrainment water weir system, which simulated infinite lateral boundaries. Surface drogue Particle Tracking Velocimetry (PTV) was used to yield large coverage, high resolution surface velocity field measurements, allowing detailed turbulence analysis. Although the time-mean plane jet observed the typical near-Gaussian velocity profile, the jet was temporally highly variable. It displayed large meanders flanked by prominent asymmetrically aligned vortices, similar to that observed in the Otago jet. This two-dimensional turbulence propagated downstream and gave the jet a ’flapping’ appearance. This two-dimensional turbulence outweighed the three dimensional turbulence from five exit widths downstream and as BF increased (lower AR and/or higher Re) the across-jet turbulent velocity component magnitude grew relative to its along-jet counterpart. The flapping made the jet appear wider than accounted for by its entrainment, due to the lateral smearing of the velocity profile. As AR decreased the entrainment relative to the jet’s lateral growth, decreased even further, causing the along-jet velocity similarity profile to deviate from the common Gaussian profile towards an increasingly squarer shape. As BF increased the flapping occurred more regularly and a dominant flapping frequency developed giving the jet a major Strouhal number (St) of around 0.09. This St decreased notably with decreasing AR, which could have been the cause for the squarer velocity profiles due to decreased mixing through decreased vortex production. The jet’s meanders were compressed with downstream distance, giving them smaller wavelengths and larger amplitudes. This compression increased with increasing BF, as did the flapping amplitude and purity, while the flapping advection velocity decreased. In summary, the laboratory results show that shallowness greatly influences a plane jet’s velocity field, particularly its two-dimensional turbulence, which will have to be incorporated in any future shallow jet theoretical or numerical models. Future ADCP studies of ebb jets are recommended to employ sampling frequencies fine enough to resolve such features.