Effect of polymer additives on dynamics of water level in an open channel.

The presence of a tiny amount of polymers (a few parts per million) in a fluid dramatically reduces turbulent drag. For this reason, polymer additives have been proposed to be used in flood remediation: in an open channel at a fixed flow rate, the decrease in friction due to polymer addition is expected to lead to a decrease in water height in the channel. However, in a recent field experiment, a counterintuitive transient increase in water height has been observed downstream of polymer injection, with the amplitude and duration of the height increases being the largest far downstream of the injection point. We numerically investigate the effect of polymer additives on the water height in a long channel using the shallow water equations augmented with an evolution equation for polymer concentration that incorporates turbulent dispersion and polymer degradation, as well as a friction coefficient that decreases with increasing polymer concentration. The model predicts the existence of a region originating at the polymer injection point and propagating downstream at the fluid velocity in which the height overshoots before decreasing. This region spreads and grows in amplitude with a downstream position, consistent with experimental observations. We elucidate the mechanism of this unexpected rise in water height in the channel and illustrate it with a simple model. The reduction in friction due to polymer injection leads to fluid acceleration. Therefore, the fast-moving fluid upstream runs into slow-moving fluid downstream, leading to the transient "piling up" of the fluid just downstream of the region of polymer-laden fluid, and hence to the emergence of the height overshoot. We also suggest a technique to mitigate the water rise, as this is detrimental to practical applications. • Polymer additives may aid in mitigating flooding by increasing drainage capacity. • Polymer injection in an open channel exhibits a transient water height overshoot. • Modified shallow water equations capture all the aspects of water height dynamics. • The interplay between fluid inertia and drag reduction induces height overshoot. • Along with the mechanism of overshoot, we describe techniques to mitigate it. [ABSTRACT FROM AUTHOR]