Abstract
A rapid downstream weakening of the processes that drive the intensity of transverse mixing at the confluence of large rivers has been identified in the literature and attributed to the progressive reduction in channel scale secondary circulation and shear-driven mixing with distance downstream from the junction. These processes are investigated in this paper using a three-dimensional computation of the Reynolds averaged Navier Stokes equations combined with a Reynolds stress turbulence model for the confluence of the Kama and Vishera rivers in the Russian Urals. Simulations were carried out for three different configurations: an idealized planform with a rectangular cross-section (R), the natural planform with a rectangular cross-section (P), and the natural planform with the measured bathymetry (N), each one for three different discharge ratios. Results show that in the idealized configuration (R), the initial vortices that form due to channel-scale pressure gradients decline rapidly with distance downstream. Mixing is slow and incomplete at more than 10 multiples of channel width downstream from the junction corner. However, when the natural planform and bathymetry are introduced (N), rates of mixing increase dramatically at the junction corner and are maintained with distance downstream. Comparison with the P case suggests that it is the bathymetry that drives the most rapid mixing and notably when the discharge ratio is such that a single channel-scale vortex develops aided by curvature in the post junction channel. This effect is strongest when the discharge of the tributary that has the same direction of curvature as the post junction channel is greatest. A comprehensive set of field data are required to test this conclusion. If it holds, theoretical models of mixing processes in rivers will need to take into account the effects of bathymetry upon the interaction between river discharge ratio, secondary circulation development, and mixing rates.
Highlights
It has been noted for some time that two confluent rivers can take some significant distance downstream to mix completely [1,2,3,4,5,6,7]
For the R simulations, the river remains poorly mixed throughout all the domain for all three discharge ratios
For all three of the discharge ratios considered in this study, significant mixing had occurred within 8000 m of the junction in the N case, with measured planform and bathymetry, that is about 8 multiples of the post confluence channel width
Summary
It has been noted for some time that two confluent rivers can take some significant distance downstream to mix completely [1,2,3,4,5,6,7]. Basic semi-theoretical reasoning explains why, in the absence of other forcing factors, the mixing distances of large rivers should be long and this is because far field mixing processes on their own are not effective. Theoretical analyses have shown that the rate of transverse (turbulent) diffusion, and the distance required in the downstream direction, is a function of the square of post-confluence width [5,13,14]. This distance may be greater with higher flow momentum and lower with a higher diffusion coefficient [13]
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