  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 far downstream of polymer injection. We numerically investigate
the effect of polymer additives on the water height in a long canal using the
shallow water equations augmented with an evolution equation for polymer
concentration that incorporates turbulent dispersion and polymer degradation.
Just downstream of polymer injection, the water height decreases due to the
decreased friction at a fixed volumetric flow rate. Further downstream,
however, the height can increase, consistent with the experimental observation.
We elucidate the mechanism of this unexpected rise in water height in the
canal. We also suggest a technique to mitigate the water rise, as this is
detrimental for practical applications.
