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.

流体中存在微量聚合物（百万分之几）可显着减少湍流阻力。因此，聚合物添加剂被提议用于洪水修复：在固定流量的明渠中，由于聚合物添加而导致的摩擦力减少预计会导致渠道内水位的降低。然而，在最近的现场实验中，在聚合物注入下游观察到了违反直觉的水位高度瞬时增加，高度增加的幅度和持续时间在注入点下游处最大。我们使用浅水方程以及聚合物浓度演化方程来数值研究聚合物添加剂对长通道中水位高度的影响结合了湍流分散和聚合物降解以及摩擦系数随着聚合物浓度的增加而降低。该模型预测存在一个源自聚合物注入点并以流体速度向下游传播的区域，其中高度在下降之前超调。该区域随下游位置扩散和增大，与实验观察结果一致。我们阐明了河道水位意外上升的机制，并用一个简单的模型进行了说明。由于聚合物注入而减少的摩擦导致流体加速。因此，上游快速移动的流体遇到下游缓慢移动的流体，导致流体在负载聚合物的流体区域的下游瞬时“堆积”，从而出现高度超调。我们还建议了一种减轻水位上​​升的技术，