A laboratory study of buoyant fresh-water boundary currents in tidal cross-flows

Peter Davies, T. G. A. Jacobs, Linus A. Mofor

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Laboratory modelling experiments have been conducted to simulate the behaviour and stability characteristics of a buoyant boundary current formed by the discharge of river water into a tidal crossflow. Results from parametric studies of conditions typical of the Channel are presented to show: a) the different forms taken by the boundary currents for stable and unstable currents respectively; b) the dependence of the nose velocity and current width of the boundary current upon the driving density difference and the amplitude of the tidal forcing; and c) variation with Burger number Bu of the growth rate and wavelength of the meander-like instabilities. Measurements are also presented to show the spatial and temporal development of the boundary current depth, for a range of external forcing conditions. The boundary current is shown to develop in three stages, in the first of which the nose moves with the appropriate constant gravity current speed. The second stage is characterised by a decay with time t and along-shore distance x of the nose velocity U(N)(x,t) as frictional stresses assume importance. Scaling arguments are advanced to predict a decay with t-1/4 and x-1/4 for U(N), and the results show fair agreement with this prediction. In the final stage of development the driving buoyancy pressure gradient is weak and the nose velocity is controlled principally by the tidal forcing. The data show that the spatially-averaged nose velocity, scaled with the gravity current velocity: 1) increases with increasing Rossby number Ro; and 2) decreases with increasing Burger number. The mean width lambda (x0, t) of the boundary current at a given along-shore reference station x0 is shown to increase with time as predicted by simple scaling considerations, but there is significant quantitative discrepancy in the growth mte; the much stronger lateral growth than predicted is ascribed to deficiencies in the viscous dissipation model and neglect of interfacial mixing. No dependence on Bu is found for the growth rate of the current width lambda (x0, y0, t) which varied roughly from 0.6 to 4.0 times the internal Rossby radius of deformation R(d). The time-averaged boundary current width, scaled with R(d), is shown to decrease with increasing Bu and Ro, and the boundary current depth h (x0, y0, t) at a fixed along-shore location (x0 y0), is shown to increase with time at a rate which decreases with increasing Bu. The amplitudes of boundary current instabilities are found to decrease with increasing Bu only for high values of Ro. In these cases, the instabilities are judged to be barotropic. The wavelengths of the unstable flows, scaled with Rd, appear to decrease with increasing Bu and with decreasing Ro. Agreement is found with measurements made by Griffiths and Linden [1982] for the ratio of wavelength and boundary current width at high Ro.
Original languageEnglish
Pages (from-to)489-503
Number of pages15
JournalOceanologica Acta
Issue number5-6
Publication statusPublished - 1993


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