Effect of bed elevation discordance on momentum-flux from tributary flow and parameter values in 1d confluence models

Abstract

Bathymetric surveys in confluences of both alluvial and mountaneous rivers have shown that a bed step at a tributary entrance to the confluence is a common morphological feature and that it may also develop in the main-river. Thus, this paper aims at studying how the presence of the bed step in either upstream channel and the extent of bed elevation discordance (i.e. bed step height) affect contribution of the tributary flow to the 1D momentum equation. To this aim, a 3D model is used to find distributions of the flow angle and the momentumflux in the downstream cross-section of the tributary under three possible scenarios in the confluence: DR = QR / Qn = {0,250; 0,583; 0,750}, where QR and Qn are flow discharges in the main-river upstream and downstrem of the confluence. Effects of three extents of bed elevation discordance in both channels are analysed: ΔzP / hn = {0,10; 0,25; 0,50} and ΔzR / hn = {0,10; 0,25; 0,50}, where ΔzP and ΔzR stand for bed step heights in the tributary and the main-river and hn stands for the flow depth in the main-river at the confluence. Distributions are used to calculate the component of the tributary force of inertia that acts in tha main-river direction IPx, and parameters of 1D confluence models that are used for its estimation, i.e. the mean cross-sectional flow angle δ and σ - the correction coefficient for this angle. It is found that the bed step in the tributary and the step with the heighest extent of bed elevation discordance in the river reduce contribution of the tributary flow to 1D momentum equation from 8% to 58%, while that in the main-river with low and moderate extent increase its contribution by 15-30% depending on the DR-value. It is also shown that the value of Hager's correction coefficient σ is not constant. It rather depends on both parameters (DR and Δz / hn). In that respect the bestfitting curves σ(DR) are found for each cascade.

Hidrografska merenja na ušćima aluvijalnih i planinskih vodotoka pokazala su da je podvodna kaskada na spoju pritoke sa rekom uobičajena pojava, kao i to da može postojati i u koritu matične reke na spoju sa pritokom. Cilj ovog rada je da ispita kako položaj i visina kaskade utiču na doprinos pritoke dinamičkoj jednačini u linijskim modelima ušća. Pomoću modela prostornog tečenja utvrđeni su rasporedi ugla skretanja toka i protoka količine kretanja u nizvodnom preseku pritoke za tri stepena izdignutosti dna pritoke, odnosno reke ΔzP / hn = {0,10; 0,25; 0,50} i ΔzR / hn = {0,10; 0,25; 0,50} gde su ΔzP i ΔzR visine kaskada u pritoci i reci, a hn dubina vode u reci na ušću, i tri moguća hidrološka scenarija DR = QR / Qn = {0,250; 0,583; 0,750}, gde su QR i Qn protoci u reci uzvodno i nizvodno od ušća. Na osnovu ovih rasporeda određeni su: komponenta sile inercije pritoke u pravcu osovine reke IPx i vrednosti parametara pomoću kojih se u linijskim modelima ušća obuhvata uticaj pritoke, a to su srednja vrednost ugla skretanja toka u nizvodnom preseku pritoke δ i σ - koeficijent neravnomernosti ovog ugla. Utvrđeno je da kaskada u pritoci i kaskada sa najvišim stepenom izdignutosti u reci smanjuju uticaj pritoke u dinamičkoj jednačini od 8% do čak 58%, dok kaskade u reci sa niskim i umerenim stepenom izdignutosti u zavisnosti od DR povećavaju njen doprinos za 15-30%. Pokazano je da Hagerov koeficijent σ nema konstantnu vrednost i da zavisi od oba prametra (DR i Δz / hn). Za svaku kaskadu određene su zavisnosti σ(DR).