Analytical representations of the Residence Time Distribution associated
with hyporheic exchange beneath dune-like bedforms for different
normalized sediment bed depths and groundwater underflow velocities.
Abstract
The hyporheic exchange below dune-shaped bedforms has a great impact on
the stream environment. One of the most important properties of the
hyporheic zone is the residence time distribution (RTD) of flow paths in
the sediment domain. Here, we evaluate the influence of dimensionless
sediment depths d b * = 2 π d b / λ where λ is the dune wavelength and
different values of dimensionless groundwater underflow values u b *
(similar to dune migration celerity), on the shape of the hyporheic
exchange RTD. Empirical RTDs were generated, over a range of
combinations between d b * and u b * values, from numerical
particle tracking experiments in which 10000 particles were released
over a flat domain. These empirical RTDs are represented by different
distributions over the range of d b * and u b * . A Fréchet RTD is
the best fit for deep beds ( d b * >3.2) and negligible
underglow ( u b * <0.1). A LogNormal RTD is often the best
representation for u b * ≤ 0 . 8 , while a Gamma RTD performs better for
larger values of u b * . In general, a LogNormal RTD provides a good
representation of the empirical RTDs in all cases, as it is identified
as either the best or the second-best fitting distribution according to
the Anderson-Darling test. The parameters of these analytical
distributions vary with d b * and u b * , and this dependence is
graphically represented in this work. These results contribute to our
understanding of the physical and mixing processes underpinning
hyporheic exchange in streams and paves the way for a quick evaluation
of its potential impact on nutrient and contaminant processing (e.g.,
based on the magnitude of the Damköhler number).