Unravelling the hydraulics of leaky barriers: physical and mathematical modelling

Flooding is one of the great issues of our time and is the most damaging environmental hazard globally, costing over €40 billion a year in Europe alone. Solving the problem is a huge challenge. Climate change, resulting in wetter winters and more intense summer storms, is aggravating flooding. Meanwhile, demand for land to feed and house growing populations leads to increasing concentrations of people and assets in areas exposed to flooding, and ongoing land use change continues to increase the severity and frequency of flooding.

Traditionally flooding has been managed primarily through large, engineered structures, but these structures are costly to install and maintain, and often provide flood reduction benefits to the detriment of the environment, e.g., having a negative effect on wildlife and biodiversity. These consideration have, in recent years, driven a move away from such structures to multiple small-scale nature-based interventions distributed across the landscape, an example of which is the leaky barrier (LB). LBs can be used to mitigate flood risk and provide other benefits such as reducing diffuse pollution. Yet, LBs are poorly understood.

At present, there is no accepted way of representing LBs in models, although there have been attempts to put multiple LBs into hydraulic models of catchment systems. Modelling approaches include using high values of Manning’s n to represent LBs; modelling them as reductions in cross-sectional area; using combined weir/sluice gate equations; and using an equivalent ‘outlet pipe diameter’, defined by the amount of flow able to flow under, through or around the barrier as a parameter to represent leakiness. These models provide useful clues as to how combinations of features may behave in aggregate, but it is far from clear what sort of LBs they represent and there is high uncertainty associated with the results obtained.

The research discussed here combines physical and mathematical modelling to improve understanding of LB behaviour. Hydraulic flume experiments are conducted which model a range of naturally occurring and constructed LBs, including upright obstructions as a model of growing vegetation and horizontal obstructions as an analogue of log jams, woody debris barriers and beaver dams, all of which often form horizontal, or nearly horizontal, obstructions to the flow. Experiments show that barrier design has a big impact on the hydraulics. It is shown that some existing approaches, such as using an equivalent ‘outlet pipe diameter’ or a high Manning’s n were not able to capture the observed behaviour. This raises a series of questions about the sensitivity of hydraulic behaviour to various design parameters and what is required to model LBs adequately.

Data from the simplest design: the single horizontal barrier, was used to inform a finite volume model of the flume and LB. The combined weir/sluice gate equations are shown to provide a good model of a single horizontal barrier. However, the behaviour of the other LB designs is significantly different and cannot be represented adequately using this model.