Physically consistent modelling of the flow resistance across the laminar-turbulent transition allows for efficient computation of zero-inertia overland flow

Résumé fourni par la source

Flow simulations are often computationally demanding, in particular when they span periods much longer than the time scale of the flow to study the interaction with slower processes, such as vegetation growth. It is thus desirable to minimize the computational effort with appropriate strategies. One strategy is to omit insignificant terms from the model equations. In the case of overland flow, the shallow-water equations (SWE) can be reduced to the single-variable zero-inertia equation (ZIE) by omitting inertial terms. However, the integration of the ZIE becomes increasingly difficult with decreasing surface slope, and eventually stalls when the water surface is horizontal. Here, we show that the difficulties for integrating the ZIE for small slopes originate from the application of resistance relations for turbulent flow in the laminar flow regime, and that these difficulties can be overcome by consistently modelling the flow resistance, without the need of improvised modifications which have been applied previously. We propose to combine the resistance relations for laminar and turbulent flow linearly, facilitating a gradual transition which is less sensitive to the uncertainty in the transition in contrast to switching. Lastly, we demonstrate the suitability of our proposed method for simulating overland flow by applying it to a partially vegetated semi-arid hillslope at high spatial and temporal resolution of one metre, a high temporal resolution of the precipitation at one minute, over a period of ten years. Our work shows that surface flow can be modelled realistically over time spans of pattern formation in semi-arid vegetation.

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