1 DOWNSTREAM HYDRAULIC GEOMETRY of ALLUVIAL RIVERS Pierre Y. Julien Colorado State University New Orleans December 2014

Objectives Discuss the downstream hydraulic geometry of alluvial rivers in terms of: Level I – Alluvial river equilibrium Level II – Spatial width changes Level III – Temporal width changes

I – Alluvial river equilibrium Objectives: Review the Downstream Hydraulic Geometry (DHG) equations for alluvial rivers Define Downstream Hydraulic Geometry Review DHG equations Compare with field measurements Discuss some limitations of DHG

Cross-section geometry

Downstream Hydraulic Geometry

6 Some DHG equations

7 Julien-Wargadalam equations

8 Bankfull width and depth

9 Bankfull velocity and slope

10 Performance of different equations

I – Alluvial river equilibrium Conclusion: Downstream Hydraulic Geometry equations provide very good first order approximations of alluvial river equilibrium conditions.

Limitations of DHG equations Limitations of the DHG equations include: What is the dominant, bankfull or effective discharge? What grain size (d 50 or d 90 …) should be used? Can DHG equations predict meandering or braiding? Is it also appropriate to ask: Do rivers have constant W, h or S? Does equilibrium exist? Lets discuss further the width changes in space and time

Objectives: illustrate the changes in river widths and explain how river width can decrease Illustrate channel width changes in space Explain the concept of equivalent channel width Show an example on the Rio Grande II – Spatial width changes

narrow 14 wide Reach of the Rio Grande, NM

Relationship between channel width and sediment transport

Concept of equivalent widths The concept of equivalent channel width stems from the decrease in sediment transport with increased channel width: Hypothesis: The channel width of river reaches can be different from the equilibrium channel width from the DHG equations – however, to maintain the same sediment transport level, an increase in channel width requires an increase in channel slope.

17 Example on the Rio Grande, NM From Leon et al. ASCE-JHE 135(4), 2009

18 Slope vs width From Leon et al. ASCE-JHE 135(4), 2009

19 Slope vs width-depth ratio From Leon et al. ASCE-JHE 135(4), 2009

Wider reaches are steeper! From Leon et al. ASCE-JHE 135(4), 2009

II – Spatial width changes Conclusion: Channel widths can be different from equilibrium conditions, but to satisfy continuity in sediment transport, wider channels require steeper slopes.

Objectives: explain how alluvial river widths change over time Illustrate that the channel widths can change with time Explain the concept of deviation from equilibrium Show and example on the Rio Grande Estimate the time scale for river width adjustments III – Temporal width changes

Temporal Changes in Hydraulic Geometry Rio Grande below Cochiti Dam, NM Braiding Transition Meandering From Richard et al. ASCE-JHE 131(11), 2005

Hydraulic Geometry of the Rio Grande From Richard et al. ASCE-JHE 131(11), 2005

How do rivers decrease their channel width?

Rio Grande – note the channel width changes

Rio Grande

Rio Grande

Rio Grande

Temporal width changes Hypotheses: 1.The alluvial channel width gradually adjusts towards the equilibrium width. 2.The annual change in channel width is proportional to the deviation from equilibrium, measured as the difference between the current channel width and the equilibrium channel width.

Hypothesis 1. Channel widths change towards equilibrium

Hypothesis 2. Width changes are proportional to the deviation from equilibrium equilibrium

Changes in active channel width Rio Grande, NM (after Richard et al., 2005) Reach No. k1k1k1k1 k1Wek1Wek1Wek1We W e (m) R2R2R2R2 Entire Change in active channel width equilibrium Deviation from equilibrium

Prediction of Active Channel Width by Exponential equation (after Richard et al., 2005) Equilibrium width half adjustment Half adjustment Time scale  0.7/k 1

Conclusions: Channel widths gradually change toward equilibrium The annual width change is proportional to the difference between the actual width and the equilibrium width The time required to reach equilibrium is asymptotic, but half the width adjustment can be reached in 0.7/k years, with for instance k ~ on the Rio Grande. III – Temporal width changes

Conclusions I - Downstream Hydraulic Geometry equations Give very good first order approximations of alluvial river equilibrium II - Spatial changes in channel widths Channel widths can differ from equilibrium channel widths, and wider reaches require steeper slopes III - Temporal changes in channel widths Channel widths gradually change toward equilibrium at a rate proportional to the difference between the actual width and the equilibrium width The time required to reach equilibrium is asymptotic, but half the width adjustment can be reached in 0.7/k years, and k ~ on the Rio Grande

37 J. Wargadalam, CSU and DID Indonesia G. Richard, CSU and Mesa State University C. Leon, CSU and RTI U. Ji, Y.H. Shin and K.Y. Park, CSU and K-WATER D.C. Baird, R. Padilla and J. Aubuchon, USBR J.S. Lee, Hanbat University So many others… Acknowledgments

Byen Mersi ! Mersi !