Confluence of Density Currents Produced by Lock-Exchange Hassan Ismail University of South Carolina

University of South Carolina Scholar Commons Theses and Dissertations 2017 Confluence of Density Currents Produced by Lock-Exchange Hassan Ismail University of South Carolina Follow this and additional works at: https://scholarcommons.sc.edu/etd Part of the Civil Engineering Commons Recommended Citation Ismail, H.(2017). Confluence of Density Currents Produced by Lock-Exchange. (Doctoral dissertation). Retrieved from https://scholarcommons.sc.edu/etd/4416 This Open Access Dissertation is brought to you by Scholar Commons. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of Scholar Commons. For more information, please contact [email protected]. Confluence of Density Currents Produced by Lock-Exchange by Hassan Ismail Bachelor of Science University of South Carolina 2011 Master of Science University of South Carolina 2015 Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Civil Engineering College of Engineering and Computing University of South Carolina 2017 Accepted by: Jasim Imran, Major Professor M. Hanif Chaudhry, Committee Member Enrica Viparelli, Committee Member Jamil Khan, Committee Member Cheryl L. Addy, Vice Provost and Dean of the Graduate School c Copyright by Hassan Ismail, 2017 All Rights Reserved. ii Dedication For Heather. iii Acknowledgments This work was possible thanks to funding support from the National Science Foun- dation. I would like to thank my dissertation committee for their time, constructive feed- back, and guidance in completing this work. Foremost is Jasim Imran, my advisor, mentor, major professor, and collaborator on research projects through my graduate studies. His encouragement and flexibility allowed me to investigate a variety of scholarly projects through my time at the University, and what I have learned under his advisement goes far beyond the contents of the work presented here. Thank you to the members of my committee, M. Hanif Chaudhry, Enrica Viparelli, and Jamil Khan who have supported, questioned, and probed my work to ensure that I have earned this doctorate, and the work itself can be given the name "dissertation" in the truest meaning of the word. I would also like to thank the water resources research group, Department of Civil & Environmental Engineering, and the University of South Carolina. I can not think of any fellow graduate student or post-doctoral researcher in the water resources research group with whom I have not discussed, collaborated, or brain-stormed about my research. Specifically, I would like to thank Lindsey LaRocque for her guidance in the laboratory and in graduate school life. I have made a home at the University of South Carolina over the course of my studies, and I want to thank the University system which has treated me well for many years, and I hope I have and continue to represent the University with integrity and pride. Beyond academic faculty and researchers, I would like to thank the support staff iv in the Department of Civil & Environmental Engineering. Specifically I want to acknowledge Anne Kawamoto, Patrick Blake, Russell Inglett, and Karen Ammarell. Anne has always been helpful with organization of the research group. Patrick has helped with information technology needs including helping me get started with us- ing Linux operating systems which became critical to this work. Russell provided laboratory support in all studies conducted in the laboratory. Finally, Karen has helped with any procedural needs to ensure I followed all departmental and university guidelines. I tell every student that I can, "If Karen is not your best friend yet in this department, make sure she becomes that soon." Most importantly, I want to acknowledge my family. My father, Mohamad, my late mother, Randa, and my two brothers, Ahmad and Bassem: thank you all for shaping me into the man I am today. And mom, I miss you and thank you for the time we did have together. I want to thank my wife and best friend, Heather. Nothing in this work would be possible without the support given by her; I could not ask for more. Finally I would like to thank Heather for giving to me my joy, my son Gabriel. Gabriel makes me happy. Thank you for that. v Abstract Density currents represent a broad classification of flows driven by the force of gravity acting on a fluid with variable density. With examples of density currents including turbidity currents, sand storms, salt wedges in tidal rivers, and oil spills, a great deal of attention has been previously given to understanding the underlying mechanisms of such flows and implications of those flows on fluid, species, and sediment transport. Although documented confluences occur naturally in terrestrial and submarine set- tings, little attention has been given to understanding the confluence of two density currents. This study furthers the state of knowledge on density current confluences by systematically studying the unsteady flow phenomena and providing a methodology for describing the flows based on the bulk properties in the pre- and post-confluence density currents. Numerical simulations were conducted with experimental validation in which the effect of the initial density difference, channel depth, and junction angle were studied. The simulations revealed that the junction played a critical role in the combined current’s bulk properties. In the junction zone, the density currents accelerated and became thicker. After the combined front continues downstream, an elevated plume of dense fluid remained in the junction zone for some time. It was concluded for the range of densities tested, that initial density difference has little effect on the bulk properties when nondimen- sionalized. The role of the junction angle was isolated, and it is concluded that higher junction angles result in higher peak velocity in the junction zone and a larger plume. This notwithstanding, the effect of the junction is short-lived and the bulk properties vi of the combined current have little dependence on junction angle further downstream. The initial conditions (initial density, channel depth, and junction angle) are combined via a Reynolds number giving an indication of the downstream oriented inertia entering the junction zone from both upstream branches of the channel network. Trends in bulk properties as functions of this Reynolds number are presented, but at high values of Reynolds number, many bulk properties approach a constant value independent of Reynolds number. vii Table of Contents Dedication .................................. iii Acknowledgments ............................. iv Abstract ................................... vi List of Tables ................................ x List of Figures ............................... xii Chapter 1 Introduction ......................... 1 1.1 Background . 1 1.2 Outline . 7 Chapter 2 Numerical Model Description .............. 9 2.1 Governing Equations . 9 2.2 Solution Algorithm . 11 Chapter 3 Physical Experiments & Model Validation . 13 3.1 Model Set-up . 13 3.2 Results . 14 3.3 Numerical Model Performance . 15 3.4 Summary . 16 viii Chapter 4 Confluence of Density Currents in a 45◦ Junction . 21 4.1 Initial & Boundary Conditions . 21 4.2 Numerical Experiments . 22 4.3 Results & Analysis . 23 4.4 Summary . 29 Chapter 5 The Effect of Junction Angle on Density Current Confluences ......................... 53 5.1 Model Set-up . 53 5.2 Test Cases . 54 5.3 Results & Analysis . 54 5.4 Summary . 57 Chapter 6 Summary & Conclusions . 81 Bibliography ................................ 86 ix List of Tables Table 3.1 Experimental and numerical test cases and results of bulk properties. 17 Table 4.1 Case summary. D0/H0 = 1 indicates full-depth cases, and D0/H0 < 1 indicates partial-depth cases. 31 Table 4.2 Constant upstream , peak, minimum, and constant downstream head thickness for each case. Thicknesses are normalized by channel depth and position is normalized by lock length measured from the upstream wall. Empty entries indicate that no constant value was reached. 32 Table 4.3 Plume thickness results for full-depth cases. The position is measured from the upstream wall of the domain and is normalized by the lock length. 33 Table 4.4 Results of the distance from the current nose to the location of maximum plume height, ∆X . The position is measured from the upstream wall of the domain and is normalized by the lock length. 34 Table 4.5 Nose height results for full-depth cases. The position is measured from the upstream wall of the domain and is normalized by the lock length. 35 Table 4.6 Froude number summary in each phase of flow. Location values are normalized by lock length and are measured from the upstream wall. 36 Table 4.7 Summary of near-bed maximum horizontal velocity. Locations are normalized by the lock length and measured from the up- q 0 stream wall. Horizontal velocity is normalized by goHo. 37 Table 5.1 Initial conditions for each junction angle. 59 ˆ Table 5.2 Re0 for each case. 59 x Table 5.3 Froude number results for each case. The second peak and constant Froude number correspond to the post-confluence reaccel- eration phase. 60 Table 5.4 Head thickness results for each case. 61 xi List of Figures Figure 3.1 Plan and profile of the experimental flume for full- and partial- depth cases. Units are in meters. 17 Figure 3.2 Comparison of front shape for the physical experiments and simulations at 5s and 14s after the lock-gates were released. 18 Figure 3.3 Comparison of bulk properties (front position, front velocity, and front thickness) from the physical experiments and simulations. 18 Figure 3.4 Comparison of simulation output from the grid 1 and grid 2 for the full-depth case. 19 Figure 3.5 Comparison of simulation output from the grid 1 and grid 2 for the partial-depth case. 20 Figure 4.1 Computational grid and domain geometry. 38 Figure 4.2 Typical propagation of the density currents for a full-depth case (case 5).

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