Investigation of controls on secondary circulation in a simple confluence geometry using a three-dimensional numerical model

Recent research into river channel confluences has identified confluence geometry, and particularly bed discordance, as a control on confluence flow structures and mixing processes, and this has been illustrated using both field measurements in natural confluences and laboratory measurements of simplified confluences. Generalization of the results obtained from these experiments is limited by the number of confluence geometries that can be examined in a reasonable amount of time. This limitation may be overcome by numerical models, in which confluence geometry is more readily varied, and data acquired more rapidly. This paper aims to: (i) validate the application of a three-dimensional numerical model to a simple confluence geometry; (ii) simulate the effects of different boundary condition values upon flow structures; and (iii) interpret the implications of these simulations for river channel confluence dynamics. The model used in this research solves the three-dimensional form of the Navier–Stokes equations and is used to simulate the flow in a parallel confluence of unequal depth channels and to investigate the effect of different combinations of velocity and depth ratio between the two tributaries. The results generally agree with empirical evidence that secondary circulation is generated in the absence of streamline curvature, but only for specific combinations of depth and velocity ratio. This research shows how understanding of the interaction of these controls is enhanced if pressure gradients are considered. The velocity ratio is the prime determinant of the cross-stream pressure gradient that initiates cross-stream velocities. However, for significant secondary circulation to form, cross-stream velocities must lead to significant transfer of fluid in the cross-stream direction. This depends on the vertical extent of the cross-stream pressure gradient which is controlled by the depth ratio. In this study, strong secondary circulation occurred for a depth differential of 25% or more, as long as the velocity in the shallower tributary was at least as great as that in the deeper channel. This provides an important context for interpretation of previous work and for the design of new experiments in both the field and the laboratory. © 1998 John Wiley & Sons, Ltd.

[1]  J. Best,et al.  Separation Zone at Open‐Channel Junctions , 1984 .

[2]  D. Spalding.  The Computation of Flow Around Ships with Allowance for Free-Surface and Density-Gradient Effects , 1985 .

[3]  B. Launder,et al.  The numerical computation of turbulent flows , 1990 .

[4]  Leslie M. Smith,et al.  The renormalization group, the ɛ-expansion and derivation of turbulence models , 1992 .

[5]  S. Orszag,et al.  Renormalization group analysis of turbulence. I. Basic theory , 1986 .

[6]  P. Ashmore.  Anabranch confluence kinetics and sedimentation processes in gravel-braided streams , 1993, Geological Society, London, Special Publications.

[7]  Vincent H. Chu,et al.  Computation of Shallow Recirculating Flow Dominated by Friction , 1996 .

[8]  K. Richards,et al.  High resolution, two‐dimensional spatial modelling of flow processes in a multi‐thread channel , 1998 .

[9]  W. C. Reynolds,et al.  On the Yakhot-Orszag renormalization group method for deriving turbulence statistics and models , 1992 .

[10]  M. Mosley.  An Experimental Study of Channel Confluences , 1976, The Journal of Geology.

[11]  B. Kennedy.  On Playfair's law of accordant junctions , 1984 .

[12]  Jacques Ganoulis,et al.  Experimental Investigation of Shallow Recirculating Flows , 1989 .

[13]  J. Bridge,et al.  The interaction between channel geometry, water flow, sediment transport and deposition in braided rivers , 1993, Geological Society, London, Special Publications.

[14]  J. Bridge,et al.  Flow and sediment dynamics in a low sinuosity, braided river: Calamus River, Nebraska Sandhills , 1992 .

[15]  Ramon Cabrera,et al.  New Acoustic Meter for Measuring 3D Laboratory Flows , 1994 .

[16]  A. Roy,et al.  Effects of Bed Discordance on Flow Dynamics at Open Channel Confluences , 1996 .

[17]  J. Best.  Sediment transport and bed morphology at river channel confluences , 1988 .

[18]  Stuart N. Lane,et al.  Hydraulic modelling in hydrology and geomorphology: a review of high resolution approaches , 1998 .

[19]  A. Roy,et al.  Effect of bed morphology on flow mixing length at river confluences , 1995, Nature.

[20]  F. Lien,et al.  Assessment of turbulence-transport models including non-linear rng eddy-viscosity formulation and second-moment closure for flow over a backward-facing step , 1994 .

[21]  K. Richards.  A note on changes in channel geometry at tributary junctions , 1980 .

[22]  A. Roy,et al.  Bed morphology and sedimentology at the confluence of unequal depth channels , 1993 .

[23]  B. Rhoads,et al.  Flow structure at an asymmetrical stream confluence , 1995 .

[24]  A. Roy,et al.  Mixing-layer distortion at the confluence of channels of different depth , 1991, Nature.

[25]  Stuart N. Lane,et al.  Three-dimensional measurement of river channel flow processes using acoustic doppler velocimetry , 1998 .

[26]  J. Best.  Flow Dynamics at River Channel Confluences: Implications for Sediment Transport and Bed Morphology , 1987 .

[27]  Yasuyuki Shimizu,et al.  CALCULATION OF BED VARIATION IN ALLUVIAL CHANNELS , 1989 .

[28]  Bassam A. Younis,et al.  Prediction of turbulent flows in dredged trenches , 1995 .

[29]  Sam S. Y. Wang,et al.  Verification of a three-dimensional numerical model simulation of the flow in the vicinity of spur dikes , 1995 .

[30]  A. Roy,et al.  Turbulent flow structure at concordant and discordant open-channel confluences , 1996 .

[31]  M. V. Otugen,et al.  Separating and Reattaching Flow Structure in a Suddenly Expanding Rectangular Duct , 1995 .

[32]  S. Orszag,et al.  Development of turbulence models for shear flows by a double expansion technique , 1992 .

[33]  R. Ferguson,et al.  Secondary flow in anabranch confluences of a braided, gravel‐bed stream , 1992 .