\contentsline {section}{\numberline {1}Introduction}{4}{section.1}
\contentsline {section}{\numberline {2}Research Questions and Methodology}{5}{section.2}
\contentsline {section}{\numberline {3}Model Equations}{5}{section.3}
\contentsline {subsection}{\numberline {3.1}Balance Equations}{5}{subsection.3.1}
\contentsline {subsection}{\numberline {3.2}Simplifications}{7}{subsection.3.2}
\contentsline {subsection}{\numberline {3.3}Closure Relations}{7}{subsection.3.3}
\contentsline {subsubsection}{\numberline {3.3.1}Friction Slope}{7}{subsubsection.3.3.1}
\contentsline {subsubsection}{\numberline {3.3.2}Sediment Transport Rate}{7}{subsubsection.3.3.2}
\contentsline {subsubsection}{\numberline {3.3.3}Secondary Flow Terms}{9}{subsubsection.3.3.3}
\contentsline {subsubsection}{\numberline {3.3.4}Volume Fraction Content at the Interface}{11}{subsubsection.3.3.4}
\contentsline {subsection}{\numberline {3.4}Expansion of the System Equations}{11}{subsection.3.4}
\contentsline {subsubsection}{\numberline {3.4.1}Expansion of the Secondary Flow Terms in the Momentum Equations}{11}{subsubsection.3.4.1}
\contentsline {subsubsection}{\numberline {3.4.2}Expansion of the Sediment Transport Rate}{12}{subsubsection.3.4.2}
\contentsline {subsubsection}{\numberline {3.4.3}Expansion of the Source Term in the Constitutive Equation for the Secondary Flow}{12}{subsubsection.3.4.3}
\contentsline {subsubsection}{\numberline {3.4.4}Water Mass Conservation}{12}{subsubsection.3.4.4}
\contentsline {subsubsection}{\numberline {3.4.5}Water Momentum Conservation in \emph {x} Direction}{12}{subsubsection.3.4.5}
\contentsline {subsubsection}{\numberline {3.4.6}Water Momentum Conservation in \emph {y} Direction}{13}{subsubsection.3.4.6}
\contentsline {subsubsection}{\numberline {3.4.7}Constitutive Equation for the Secondary Flow}{13}{subsubsection.3.4.7}
\contentsline {subsubsection}{\numberline {3.4.8}Sediment Mass Conservation for the Entire Mixture}{13}{subsubsection.3.4.8}
\contentsline {subsubsection}{\numberline {3.4.9}Sediment Mass Conservation per Grain Size in the Active Layer}{13}{subsubsection.3.4.9}
\contentsline {subsection}{\numberline {3.5}Matrix Formulation}{13}{subsection.3.5}
\contentsline {section}{\numberline {4}Perturbation Analysis}{15}{section.4}
\contentsline {subsection}{\numberline {4.1}Linearization}{15}{subsection.4.1}
\contentsline {subsection}{\numberline {4.2}Test Using Numerical Simulations}{16}{subsection.4.2}
\contentsline {section}{\numberline {5}Results of the Perturbation Analysis}{19}{section.5}
\contentsline {subsection}{\numberline {5.1}Definition of Ill-posedness}{19}{subsection.5.1}
\contentsline {subsection}{\numberline {5.2}Secondary Flow}{20}{subsection.5.2}
\contentsline {subsection}{\numberline {5.3}Bed Slope Effect}{26}{subsection.5.3}
\contentsline {subsection}{\numberline {5.4}Mixed-size Sediment}{30}{subsection.5.4}
\contentsline {section}{\numberline {6}Ill-posedness Check in Delft3D}{32}{section.6}
\contentsline {subsection}{\numberline {6.1}Description}{33}{subsection.6.1}
\contentsline {subsection}{\numberline {6.2}Matrices Test}{34}{subsection.6.2}
\contentsline {subsection}{\numberline {6.3}Eigenvalues Test}{35}{subsection.6.3}
\contentsline {subsection}{\numberline {6.4}Output Test}{36}{subsection.6.4}
\contentsline {subsection}{\numberline {6.5}Computational Time Test}{38}{subsection.6.5}
\contentsline {section}{\numberline {7}Application to Real Scenarios}{40}{section.7}
\contentsline {subsection}{\numberline {7.1}Laboratory Scale}{40}{subsection.7.1}
\contentsline {subsubsection}{\numberline {7.1.1}Modeling of Secondary Flow}{41}{subsubsection.7.1.1}
\contentsline {subsubsection}{\numberline {7.1.2}Modeling of the Bed Slope Effects}{42}{subsubsection.7.1.2}
\contentsline {subsubsection}{\numberline {7.1.3}Modeling of a Degradational Case}{44}{subsubsection.7.1.3}
\contentsline {subsection}{\numberline {7.2}DVR Simulation}{50}{subsection.7.2}
\contentsline {section}{\numberline {8}Discussion}{55}{section.8}
\contentsline {section}{\numberline {9}Conclusions}{56}{section.9}
\contentsline {section}{\numberline {10}Recommendations}{59}{section.10}