Numerical study on the development of alternate bars in varying discharge conditions

Abstract

River bars are large-scale bedforms formed by the local deposition of sediments, the length of which scales with the channel width and the height with the water depth. They create suitable habitats for aquatic fauna and riparian vegetation, making them useful in river restoration projects. Understanding the dynamics of river bar development is required for a proper design of the restoration project and for developing a sustainable management scheme. The channel half-width-to-depth ratio is the key controlling parameter for the formation of alternate bars. Existing stability analyses define a resonance point and critical width-to-depth ratio, marking the transition between the bar regimes. Seasonal variations in the river discharge and the propagation of flood waves make the half-width-to-depth ratio a time-dependent parameter, varying over periods of days to months. This research aims to create a better understanding of the development of alternate bars in varying discharge conditions. For that, insight into the timescale of development of the bars is necessary to link this with the timescales associated with natural discharge variability. A straight river channel is modelled in Delft3D, with non-erodible banks to which a fixed perturbation is added, to trigger the formation of free bars and to which hybrid bars become fixed. In the first set of simulations, the upstream boundary condition is a constant discharge, with magnitudes between 50 and 1250 m$^3$/s, corresponding to a half-width-to-depth ratio between 77 and 8. The different types of alternate bars and the time to develop the bars are analysed from this constant-discharge analysis. The damping length and wavelength of the hybrid bars showed good agreement with the values determined from the theory of Struiksma et al. (1985). Free bars became suppressed when a hybrid bar pattern developed, showing that hybrid and free bars do not coexist locally. The resonance point is clearly obtained and assigned to a half-width-to-depth ratio of 37-38. Contrary to existing stability analyses, the critical half-width-to-depth ratio is marked by a gradual transition at half-width-to-depth ratios from 11 to 20 instead of a single value. In this transition, free bars develop with intervals of a few months. A clear difference in the development of hybrid bars and free bars results in a shorter timescale of development for free bars than for hybrid bars, which is in line with laboratory experiments (Fujita and Muramoto 1985; Crosato et al 2010). Also, in the mathematical derivations for describing the two types of bars, the distinction between an initial response (free bars, Colombini, Seminara, and Tubino (1987)) and a final stable bed (hybrid bars, Struiksma et al. (1985)) is considered. The numerical results show that free bars develop fastly when the bed becomes unstable, in the case of a relatively flat bed. The associated timescale shows little variation over the different simulations and stays around 20 days, which is in the same order of magnitude as the timescale related to seasonal variation. A pattern of hybrid bars develops in downstream direction, starting at the fixed perturbation. Based on the definition of the damping length by Struiksma et al. (1985), a theoretical expression is defined, which gives a good fit to the time at which a pattern of hybrid bars has developed. The transition of alternate bars around resonant conditions is modelled using a steadily increasing and decreasing discharge. The distinction between the timescales of hybrid and free bars results in a different response of the bars to a varying discharge. The first response of the bed in the transition from subresonant to superresonant conditions is the adaptation of free bars towards the new bar regime. A pattern of hybrid bars follows, developing in downstream direction. The reversed transition is governed by a migration of the hybrid bar pattern, making room for the damped bar pattern. The difference in the transitions between rising and falling discharge in combination with a bed adaptation after a temporal in- or decreased discharge led to a type of hysteresis in the transition around the riverbed's resonance point, which was not earlier detected. Hysteresis is ascribed to the increased bed stability when a hybrid bar pattern has developed, suppressing the formation of free bars in the transition from superresonant to subresonant conditions and to the time-lags associated with lower discharge conditions. This thesis assesses the timescales of alternate bars and the transition around the resonance point. The numerical model is able to assess both free and hybrid bars and therefore gives valuable information in the difference of their development. The difference is linked to the (linear) theories describing the bars and applied for answering the research question, showing the development of free bars should be largely influenced by discharge variation due to seasonal variation. The varying discharge simulations provided insights into the response and transition of alternate bars around resonance conditions, leading to a type of hysteresis which was not detected earlier. Recommendations are made towards increasing the river geometry complexity and discharge variation and the assessment of the transition around critical conditions to verify analyses around critical conditions.