\BOOKMARK [1][-]{section.1}{Introduction}{}% 1
\BOOKMARK [1][-]{section.2}{Research Questions and Methodology}{}% 2
\BOOKMARK [1][-]{section.3}{Model Equations}{}% 3
\BOOKMARK [2][-]{subsection.3.1}{Balance Equations}{section.3}% 4
\BOOKMARK [2][-]{subsection.3.2}{Simplifications}{section.3}% 5
\BOOKMARK [2][-]{subsection.3.3}{Closure Relations}{section.3}% 6
\BOOKMARK [3][-]{subsubsection.3.3.1}{Friction Slope}{subsection.3.3}% 7
\BOOKMARK [3][-]{subsubsection.3.3.2}{Sediment Transport Rate}{subsection.3.3}% 8
\BOOKMARK [3][-]{subsubsection.3.3.3}{Secondary Flow Terms}{subsection.3.3}% 9
\BOOKMARK [3][-]{subsubsection.3.3.4}{Volume Fraction Content at the Interface}{subsection.3.3}% 10
\BOOKMARK [2][-]{subsection.3.4}{Expansion of the System Equations}{section.3}% 11
\BOOKMARK [3][-]{subsubsection.3.4.1}{Expansion of the Secondary Flow Terms in the Momentum Equations}{subsection.3.4}% 12
\BOOKMARK [3][-]{subsubsection.3.4.2}{Expansion of the Sediment Transport Rate}{subsection.3.4}% 13
\BOOKMARK [3][-]{subsubsection.3.4.3}{Expansion of the Source Term in the Constitutive Equation for the Secondary Flow}{subsection.3.4}% 14
\BOOKMARK [3][-]{subsubsection.3.4.4}{Water Mass Conservation}{subsection.3.4}% 15
\BOOKMARK [3][-]{subsubsection.3.4.5}{Water Momentum Conservation in x Direction}{subsection.3.4}% 16
\BOOKMARK [3][-]{subsubsection.3.4.6}{Water Momentum Conservation in y Direction}{subsection.3.4}% 17
\BOOKMARK [3][-]{subsubsection.3.4.7}{Constitutive Equation for the Secondary Flow}{subsection.3.4}% 18
\BOOKMARK [3][-]{subsubsection.3.4.8}{Sediment Mass Conservation for the Entire Mixture}{subsection.3.4}% 19
\BOOKMARK [3][-]{subsubsection.3.4.9}{Sediment Mass Conservation per Grain Size in the Active Layer}{subsection.3.4}% 20
\BOOKMARK [2][-]{subsection.3.5}{Matrix Formulation}{section.3}% 21
\BOOKMARK [1][-]{section.4}{Perturbation Analysis}{}% 22
\BOOKMARK [2][-]{subsection.4.1}{Linearization}{section.4}% 23
\BOOKMARK [2][-]{subsection.4.2}{Test Using Numerical Simulations}{section.4}% 24
\BOOKMARK [1][-]{section.5}{Results of the Perturbation Analysis}{}% 25
\BOOKMARK [2][-]{subsection.5.1}{Definition of Ill-posedness}{section.5}% 26
\BOOKMARK [2][-]{subsection.5.2}{Secondary Flow}{section.5}% 27
\BOOKMARK [2][-]{subsection.5.3}{Bed Slope Effect}{section.5}% 28
\BOOKMARK [2][-]{subsection.5.4}{Mixed-size Sediment}{section.5}% 29
\BOOKMARK [1][-]{section.6}{Ill-posedness Check in Delft3D}{}% 30
\BOOKMARK [2][-]{subsection.6.1}{Description}{section.6}% 31
\BOOKMARK [2][-]{subsection.6.2}{Matrices Test}{section.6}% 32
\BOOKMARK [2][-]{subsection.6.3}{Eigenvalues Test}{section.6}% 33
\BOOKMARK [2][-]{subsection.6.4}{Output Test}{section.6}% 34
\BOOKMARK [2][-]{subsection.6.5}{Computational Time Test}{section.6}% 35
\BOOKMARK [1][-]{section.7}{Application to Real Scenarios}{}% 36
\BOOKMARK [2][-]{subsection.7.1}{Laboratory Scale}{section.7}% 37
\BOOKMARK [3][-]{subsubsection.7.1.1}{Modeling of Secondary Flow}{subsection.7.1}% 38
\BOOKMARK [3][-]{subsubsection.7.1.2}{Modeling of the Bed Slope Effects}{subsection.7.1}% 39
\BOOKMARK [3][-]{subsubsection.7.1.3}{Modeling of a Degradational Case}{subsection.7.1}% 40
\BOOKMARK [2][-]{subsection.7.2}{DVR Simulation}{section.7}% 41
\BOOKMARK [1][-]{section.8}{Discussion}{}% 42
\BOOKMARK [1][-]{section.9}{Conclusions}{}% 43
\BOOKMARK [1][-]{section.10}{Recommendations}{}% 44