(cid:13)c Copyright 2015 Anthony Poggioli Hydrodynamics and Sediment Transport at the River-Ocean Interface: Analytical and Laboratory Investigations Anthony Poggioli A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy University of Washington 2015 Reading Committee: Alexander R. Horner-Devine, Chair James Thomson Peter Rhines Program Authorized to Offer Degree: Civil & Environmental Engineering University of Washington Abstract Hydrodynamics and Sediment Transport at the River-Ocean Interface: Analytical and Laboratory Investigations Anthony Poggioli Chair of the Supervisory Committee: Allan and Inger Osberg Associate Professor Alexander R. Horner-Devine Civil & Environmental Engineering Thisstudypresentsacombinationofnumericalandanalyticalinvestigationsoffluidandsed- iment transport mechanics through the river-ocean interface. This region is defined broadly as the region within the river that is influenced by the receiving basin–both the salinity and the oscillating and mean basin heights–as well as the portion of the river influenced by the presence of a distinct fluvial buoyant water mass. More narrowly, we consider in this study an atidal salt wedge, the upstream hydraulic transition zone in the unstratified river, and the near-field river plume. The first main chapter presents a hydraulic model of the salt wedge estuary in sloped and landward-converging channels. It is found that the non-dimensionalized intrusion length is a function of the freshwater Froude number F , as noted in previous studies, as well as new f parameters describing the channel geometry. Further, it is found that the primary geometric influence on the intrusion length is the channel bottom slope. Comparison to field data is given indicating that the influence of nonzero bottom slope may account for the discrepancy between observation and the canonical flat estuary theory (Schijf & Scho¨nfeld, 1953). Next, we link our hydraulic model of the salt wedge to a hydraulic model of the upstream river transition zone, which is influenced by the depth of the receiving basin and is not in normal flow. We add to this a parameterization of total sediment transport in the unstrat- ified river (Engelund & Hansen, 1967) and a newly developed hydraulic model of sediment transport in the salt wedge. The model retains the key mechanistic features of sediment transport in highly stratified estuaries and is ideal for morphodynamic applications. We find that the principle influence of the salt wedge is an increase in net deposition in the lower river and the introduction of a secondary maximum aggradation length scale in addition to the backwater length discussed in Chatanantavet et al. (2012). Finally, we present experimental simulations of the steady state estuary and river plume. Theresultsoftheestuaryexperimentsquantifytheinfluenceofbottomslopeonthereduction of sensitivity of intrusion length to river discharge and confirm the results of the hydraulic model. The plume experiments indicate that the plume transitions to a jet-like outflow for sufficientlylargevaluesofF inwhichthespreadingrateisdeterminedbylateralentrainment f instead of the plume buoyancy and the liftoff is pushed far offshore. This transition is not gradual but rather step-like, being concentrated on one value (or a narrow band of values of) F . Both this critical value of F and the jet spreading rate depend crucially on the f f plume inflow aspect ratio. This jet-like behavior is anticipated to have crucial implications for delta progradation processes and the magnitude of sediment erosion in the lower river during flood events. TABLE OF CONTENTS Page List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x Chapter 1: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.0.1 Definition of the River-Ocean Interface . . . . . . . . . . . . . . . . . 3 1.0.2 Layout of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Chapter 2: Salt Wedge Hydraulics in Sloping and Converging Estuaries . . . . . . 7 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2.1 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2.2 Non-Dimensionalization of Governing Equations . . . . . . . . . . . . 12 2.2.3 Solution Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.3 Solution for a Flat Estuary of Uniform Width . . . . . . . . . . . . . . . . . 14 2.4 Solution for a Sloped Estuary of Uniform Width . . . . . . . . . . . . . . . . 16 2.5 Solution for Flat and Sloped Estuaries of Converging Width . . . . . . . . . 19 2.5.1 Existence of Hydraulic Solutions in a Converging Estuary . . . . . . . 19 2.5.2 Length-Discharge Relationship . . . . . . . . . . . . . . . . . . . . . . 21 2.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.6.1 Slope-Limitation and Estuary Convergence . . . . . . . . . . . . . . . 24 2.6.2 Comparison of L vs. Q to Real Estuaries . . . . . . . . . . . . . . . . 25 2.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Chapter 3: Hydraulic Model of Sediment Transport in the Salt Wedge . . . . . . . 44 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.2 Hydrodynamic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 i 3.2.1 Salt Wedge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.2.2 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 3.2.3 Unstratified River . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 3.2.4 Non-Dimensionalization . . . . . . . . . . . . . . . . . . . . . . . . . 50 3.3 Sediment Model Development . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3.3.1 Unstratified River . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3.3.2 Salt Wedge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.4.1 Export of Sediment to the Shelf . . . . . . . . . . . . . . . . . . . . . 56 3.4.2 Deposition of Sediment in the River . . . . . . . . . . . . . . . . . . . 58 3.4.3 Location of Maximum Deposition . . . . . . . . . . . . . . . . . . . . 60 3.5 Discussion and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Chapter 4: Experimental Simulation of the Salt Wedge and Plume . . . . . . . . . 73 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 4.2 Theoretical Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 4.3 Experimental Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 4.4.1 Salt Wedge Intrusion Length . . . . . . . . . . . . . . . . . . . . . . . 81 4.4.2 Plume Spreading and Liftoff . . . . . . . . . . . . . . . . . . . . . . . 87 4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 Chapter 5: Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 Appendix A: Sediment Model–Derivation of f , E, and E . . . . . . . . . . . . . 112 D toe ii LIST OF FIGURES Figure Number Page 1.1 A schematic illustrating the river-ocean interface, comprising the hydraulic transition zone of the lower river, the estuary, and the buoyant river plume that forms seaward of the river mouth, in side (top) and plan view (bottom). Theinterfaceindicatedinthefigureisbetweenfreshandsaltwater. Theplume can be further divided into the near-field, the initial energetic discharge re- gion, relatively insensitive to rotational forcing and ambient coastal currents, a far-field, characterized by along-coast transport in geostrophic balance, and a transitional mid-field, characterized by the formation of a retentive anticy- clonic gyre, the bulge. We focus here only on the near-field. . . . . . . . . . 6 2.1 Comparison of length-discharge solution for flat, prismatic estuary (Schijf & Scho¨nfeld, 1953), the n = 2 line, to field (Fraser, from Ward (1976), and Duwamish, from McKeon et al. (2014)) and numerical model (Merrimack, from Ralston et al. (2010)) data. Best-fit exponents for each estuary are shown. 33 2.2 (Left) side view sketch and (right) plan view sketches of model configura- tion. Independent and dependent model variables are shown. The plan view shows the two width configurations considered here–uniform, top right, and converging, bottom right. The thick-lined triangles indicate hydraulic control. 34 2.3 a) Non-dimensionalized intrusion length L versus freshwater Froude number ∗ F for a flat estuary of uniform width (Schijf & Scho¨nfeld, 1953). The L ∼ f ∗ F−2 and ∼ F−2.5 lines are also plotted. b) Normalized salt wedge shape f f (Harleman, 1961) for several values of F . . . . . . . . . . . . . . . . . . . . 35 f 2.4 Comparison of interface profile with Harleman (1961) flat bottom solution. Panelsa), c), ande)showthreeexamplemodelrunswithincreasingfreshwater Froude number in a sloped estuary of uniform width. The dashed purple, solid purple, and gray lines correspond to the density interface, channel bottom, and free surface, respectively. Panels b), d), and f) show the Harleman (1961) solution for a flat estuary with a rigid lid for the same freshwater Froude numbers. The horizontal dimension of each column is scaled with the distance shown on the x-axis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 iii 2.5 Intrusionlengthinachannelofuniformwidthandnonzeromeanbottomslope α. The curves are segregated by the value of the parameter C /α. The flat i estuary solution (Schijf & Scho¨nfeld, 1953) is also shown. This corresponds to the limit C /α → ∞. Also shown are the n = 0.2 and 0.6 tangent lines. . . 37 i 2.6 Intrusion length in a flat channel (α = 0) with varying convergence length a ∗ and constant convergence magnitude R = 5. The black dashed lines show c the asymptotic solutions discussed in the text. All solid curves are colored based on the value of the non-dimensionalized convergence length a . . . . . 38 ∗ 2.7 Intrusion length in a flat channel (α = 0) with constant convergence length a = 1 and variable convergence magnitude R . All solid curves are colored ∗ c based on the value of the convergence ratio R . The R = 1 line correspons c c to the Schijf & Scho¨nfeld (1953) solution. . . . . . . . . . . . . . . . . . . . . 39 2.8 Intrusion length in a sloped channel (α (cid:54)= 0) with constant convergence length a = 1 and variable convergence magnitude R . The dashed black lines indi- ∗ c cate the prismatic channel solution (from Figure 2.5). All converging solution curves (dots) are colored based on the value of the convergence ratio R . Il- c lustrations to the right of the Figure indicate how the estuary shape changes as R is modified and a is held constant. . . . . . . . . . . . . . . . . . . . . 40 c ∗ 2.9 Intrusion length in a sloped channel (α (cid:54)= 0) with varying convergence length a and constant convergence magnitude R = 5. The solid black and dashed ∗ c gray lines indicate the asymptotic prismatic channel solutions. The black lines correspond to uniform width solutions with b = b , the width at the mouth; 0 the dashed gray lines correspond to uniform width solutions with b = b , the ∞ width in the upstream river. All converging solution curves (dots) are colored based on the value of a . Illustrations to the right of the Figure indicate how ∗ the estuary shape changes as a is modified and R is held constant. . . . . . 41 ∗ c 2.10 a) Schematic showing slope-limited salt wedge. b) Schematic showing location of the transition zone. For L < a, the intrusion is set by the width at the mouth b . For L > 10a, the intrusion is set by the width in the upstream river 0 b . In between, the intrusion length transitions between these two asymptotic ∞ solutions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 iv 2.11 Top-width profiles of the a) Merrimack and c) Duwamish (solid black), salt wedge toe locations as function of discharge (solid, colored), and simplified width profile used in analysis (gray, dashed). b) Comparison of Merrimack numerical model data (Ralston et al., 2010, gray-blue dots) to flat, prismatic estuary solution (Schijf & Sch¨onfeld, 1953, dashed gray) and current solu- tion without (solid black) and with (light blue dot-dash) variable width. d) Comparison of Duwamish field data (gray-blue dots) to the current solution assuming either control at the mouth and constant width (dot-dash gray) or variable width and control location (solid black). . . . . . . . . . . . . . . . . 43 3.1 Schematic illustrating the free surface and mean flow profiles in the hydraulic transition and normal flow zones for backwater and drawdown events. The transition length is designated L and is a function of river discharge Q, bed t slope S , and the shoreline depth h . Normal flow and net sediment bypass 0 S exist upstream of the hydraulic transition zone. Whether the hydraulic transi- tionzoneisinbackwater(deceleration, deposition)ordrawdown(acceleration, erosion) is determined by the ratio of the normal depth h to the shoreline N depth h . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 S 3.2 Schematic illustrating the a) side and b) plan view geometry of the hydro- dynamic model. Also indicated are all independent and dependent hydrody- namic variables. The interface indicated in the Figure is that between fresh and saltwater; the intrusion landward of the mouth is the salt wedge. . . . . 65 3.3 a) Schematic illustrating the salt wedge sediment model. The sediment is modeled as a homogeneous plug of settling velocity w . The height of the s plug is assumed to be the local freshwater layer thickness h (x), accounting 1 for the tendency of the sediment to be advected over the salt wedge. The ratio of distance settled by the plug ξ to the freshwater depth at the mouth h (x = 0) = (q2/g(cid:48))1/3 gives the deposition fraction f in the estuary. b) 1 D Schematic illustrating the upstream and estuary control volumes; also shown is the sediment flux into the upstream river (numerically unity because it is normalized by the normal flow flux), the deposition flux in the upstream river (D ), the export of sediment from the upstream river to the salt wedge (E ), u toe the deposition flux in the estuary (D ), and the export to the shelf E. . . . . 66 e v 3.4 Export from the channel to the shelf E normalized by the export predicted if salt wedge formation is neglected E as a function of freshwater Froude 0 number, which varies directly with the river discharge Q. The curves are colored by the value of F , and the corresponding approximate value of the N slope S is shown next to the colorbar, assuming C = 3(10−3). All curves are 0 b calculated assuming Ro = 2, as noted in the Figure. The inset plot shows d the same curves with the axes truncated, indicating that export is enhanced for F >∼ 0.4 (see text). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 N 3.5 Export from the channel to the shelf E normalized by the export predicted if salt wedge formation is neglected E as a function of freshwater Froude 0 number. Each curve corresponds to a different value of the densimetric Rouse number, Ro ; from top to bottom, Ro = 1, 2, 3, 10. All curves are calculated d d for F = 1, as noted in the Figure. The inset plot shows the Ro = 10 curve, N d indicating that export is enhanced even at this value of Ro when F = 1. . 68 d N 3.6 Deposition in the lower river (hydraulic transition zone and estuary) D nor- malized by the deposition predicted if salt wedge formation is neglected D as 0 a function of freshwater Froude number. The curves are colored by F , and N the corresponding approximate value of the slope S is shown next to the col- 0 orbar, assuming C = 3(10−3). All curves are calculated assuming Ro = 2, b d as noted in the Figure. The values of F corresponding to the two curves N showing the greatest modification of deposition are shown next to the verti- cal discontinuities in these curves (lower right). On the F = 0.1 curve, the N regions where the salt wedge is fully depositional (f = 1) and is not fully D depositional (f < 1), as well as where the river transitions from backwater D (b.w.) to drawdown (d.d.) at h /h = 1, are indicated. The inset shows the S N deposition normalized by the normal flow sediment flux with and without the salt wedge D, D for F = 0.1. . . . . . . . . . . . . . . . . . . . . . . . . . 69 0 N 3.7 Plots of the difference in total deposition in the lower river and deposition in the estuary caused by estuary formation, D−D and D −D , respectively. 0 e e0 The total deposition anomaly (D−D ) curve is colored according to whether 0 the river is net depositional (blue, D > 0) or erosional (red, D < 0). Labeled are regions of enhanced deposition and diminished erosion outside of the es- tuary. The vertical dashed gray line indicates the the value of F for which f h /h = 1, which would indicate transition from backwater to drawdown S N (with increasing F / Q) if no salt wedge formed. These curves are calculated f for F = 0.1, as indicated. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 N vi