Secondary currents are one of the important features that characterize flow in river bends and confluences. Fluid particles follow a helical path instead of moving nearly parallel to the axis of the channel. The local imbalance between the vertically varying centrifugal force and the cross-stream pressure gradient results in generating the secondary flow and raising a typical motion of the helical flow. A number of studies, including experimental or mathematical, have been conducted to examine flow characteristics in curved open channels, river meanders, or confluences. In this research, the influence of secondary currents is studied on the elevation of water surface and the hydraulic structures in channel bends and confluences by employing a 3D OpenFOAM numerical model. The research implements the 3D OpenFOAM numerical model to simulate the horizontal distribution of the flow in curved rivers. In addition, the progress in unraveling and understanding the bend dynamics is considered. The finite volume method in (OpenFOAM) software is used to simulate and examine the behavior of secondary current in channel bends and confluences. Thereafter, a comparison between the experimental data and a numerical model is conducted. Two sets of experimental data are used; the data provided by Rozovskii (1961) for sharply curved channel, and the dataset provided by Shumate (1998) for confluent channel. Two solvers in (OpenFOAM) software were selected to solve the problem regarding the experiment; InterFoam and PisoFoam. The InterFoam is a transient solver for incompressible flow that is used with open channel flow and Free Surface Model. The PisoFoam is a transient solver for incompressible flow that is used with closed channel flow and Rigid-Lid Model. Various turbulence models (i.e. Standard k-ε, Realizable k-ε, LRR, and LES) are applied in the numerical model to assess the accuracy of turbulence models in predicting the behaviour of the flow in channel bends and confluences. The accuracies of various turbulence models are examined and discussed.

Model-H is used to describe structures found in the phase separation in films of binary liquid mixture that have a surface that is free to deform and also may energetically prefer one of the components. The film rests on a solid smooth substrate that has no preference for any component. On the one hand the study focuses on static aspects by investigating steady states that are characterised by their concentration and film height profiles. A large variety of such states are systematically analysed by numerically constructing bifurcation diagrams in dependence of a number of control parameters. The numerical method used is based on minimising the free energy functional at given constraints within a finite element method for a variable domain shape. The structure of the bifurcation diagrams is related to the symmetry properties of the individual solutions on the various branches. On the other hand the full time dependent model-H is linearised about selected steady states, in particular, the laterally invariant, i.e.\ layered states. The resulting dispersion relations are discussed and related to the corresponding bifurcation points of the steady states. In general, the results do well agree and confirm each other. The described analysis is performed for a number of important cases whose comparison allows us to gain an advanced understanding of the system behaviour: We distinguish the critical and off-critical case that correspond to zero and non-zero mean concentration, respectively. In the critical case the investigation focuses on (i) flat films without surface bias, (ii) flat films with surface bias, (iii) height-modulated films without surface bias, and (iv) height-modulated films with surface bias. Each case is analysed for several mean film heights and (if applicable) energetic bias at the free surface using the lateral domain size as main control parameter. Linear stability analyses of layered films and symmetry considerations are used to understand the structures of the determined bifurcation diagrams. For off-critical mixtures our study is more restricted. There we consider height-modulated films without and with surface bias for several mean film heights and (if applicable) energetic bias employing the mean concentration as main control parameter.