Hydraulic properties of a bifurcated channel system with

Hydraulic properties of a bifurcated channel system with different bed slopes under sub-critical flow Graduate School of Hokkaido University Kenya Kobayashi Kazuyoshi Hasegawa Kaoru Moriya

Table of contents 1. Motivation Early studies and purpose 2. Momentum analysis model 3. Experiment Flat-bed and movable-bed experiment 4. Summary

Motivation Early studies • The mechanisms of alternation under super-critical flow have been investigated by Hasegawa et al. • The hydraulic properties at a channel bifurcation under sub-critical flow have been investigated by Bolla, Repetto, and Tubino. Purpose Mainstream alternation in terms of the hydraulic properties of a bifurcated channel under sub-critical flow.

Bifurcation model Water discharge ratio r =Qb/Q

Momentum equations Momentum term Pressure term (1) Friction term Gravitational term (2)

Continuity equations (3) (4)

Solutions for momentum equations Solution under sub-critical flow Solution under super-critical flow

Water discharge ratio r plotted against the ratio of bed slopes ib/ia ib=1/531, Q=2. 0(liter/sec)

Water depth h 0 plotted against the ratio of bed slopes ib/ia ib=1/531, Q=2. 0(liter/sec)

Water discharge ratio r plotted against water discharge Q ia=1/724, ib=1/531

Comparison between theoretical and uniform flow water depth ia=1/724, ib=1/531

Experimental setup

Flat–bed experimental conditions Water discharge Q(liter/sec) Bed slope of flume a Bed slope of flume b Frude number Shields stress ia ib Fr t* Run 1 -1 1. 87 1/724 1/531 0. 453 0. 035 Run 1 -2 2. 84 1/724 1/531 0. 416 0. 049 Run 2 -1 1. 68 1/1110 1/531 0. 453 0. 032 Run 2 -2 2. 57 1/1110 1/531 0. 524 0. 039 Run 3 -1 0. 96 1/2448 1/531 0. 360 0. 026 Run 3 -2 1. 63 1/2448 1/531 0. 378 0. 036

Water discharge plotted versus time ia=1/724 ia=1/1110 ia=1/2448

Comparison between experimental and theoretical results

Movable-bed experimental conditions

Water discharge plotted versus time ia=1/724 Q ia=1/1110 ia=1/2448

Summary l. We applied momentum equations to a bifurcation model and results show that the system have two solutions for discharge ratio and water depth: one for sub-critical flow, and the other for supercritical flow. l. Results of flat-bed experiment show that the discharge ratio remains constant for each run, and that it agrees fairly well with theoretical solution l. The upstream water depth is roughly equal to uniform flow depth. However it has effect of bifurcation when the difference between bed slopes is large. l. Results of movable-bed experiments show that discharge ratio r oscillates with time for each run. l. Mainstream alternation was observed when the bed form was dune. Therefore, mainstream alternation arises from the peculiar instability of the bifurcation system, rather than from flow deviation resulting from the presence of alternating bars.