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Previous studies characterising horseshoe vortices upstream of circular cylinders in open channels have focused on changes in the Reynolds number. This study investigates the effect of the Froude number and other flow and geometrical parameters on the nature of the horseshoe vortex system that develops in front of a circular cylinder. The results show horseshoe vortex dynamics dominated by cylinder diameter, Froude number and flow depth. Instantaneous vorticity fields were classified into either two or three groups of vortex formations based on their turbulence stress magnitudes with a high dependence shown upon the Froude number and cylinder diameter. The peak stress properties of the horseshoe vortex system was found to be controlled within a certain threshold of Froude numbers (Fr ≤ 0.3 and Fr ≥ 1.7). It was also found that a single point under the horseshoe vortex can represent the vortices better than the whole field that encompasses the whole system. The characteristics of the horseshoe vortex formed upstream of a wall-mounted circular cylinder in an open channel were studied using two dimensional Particle Image Velocimetry. Experiments were conducted for different flow conditions and focused on Froude numbers, cylinder diameters, flow depths and bulk flow velocities. Two groups of experiments were conducted. The rest consisted of twenty five experiments with a wide range of Froude numbers, including sub-critical, critical and super-critical flow conditions. This group was analysed as a whole and then the lower sub-critical experiments followed by the upper sub-critical to super-critical experiments. Another set of nine sub-critical experiments were conducted focusing on the experimental design to segregate flow and geometrical parameters. Quadrant analysis was used to analyse the contribution of near-bed turbulent stresses in the region upstream of the cylinder. Applying multivariate statistical techniques, the relationship between geometrical parameters, flow conditions and the changes in the location and magnitude of the turbulent stresses under the horseshoe vortex were examined. This study, introduces the Froude number as a new governing parameter of the horseshoe vortex system, which can be important for fluvial systems with change of hydraulics regimes as mountainous rivers.

Mesh adaptation techniques are commonly coupled with the numerical schemes in an attempt to improve the modelling efficiency and capturing of the different physical scales which are involved in the shallow water flow problems. This work designs an adaptive technique that avails from the wavelets theory for transforming the local single resolution information into multiresolution information in which these data information became accessible. The adaptivity of wavelets was first comprehensively tested via using an arbitrary function in which the spatial resolution adaptivity was achieved from the local solution itself and it was based on a single user-prescribed parameter. Secondly, the adaptive technique was combined with two standard numerical modelling schemes (i.e. finite volume and discontinuous Galerkin schemes) to produce two wavelet-based adaptive schemes. These schemes are designed for modelling one-dimensional shallow water flows and are referred to the Haar wavelets finite volume (HWFV) and multiwavelet discontinuous Galerkin (MWDG) schemes. Both adaptive schemes were systematically tested using hydraulic test cases. The results demonstrated that the proposed adaptive technique could serve as lucid foundation on which to construct holistic and smart adaptive schemes for simulating real shallow water flow.