A mean residence time relationship for lateral cavities in gravel-bed rivers and streams: Incorporating streambed roughness and cavity shape

Accurate estimates of mass-exchange parameters in transient storage zones are needed to better understand and quantify solute transport and dispersion in riverine systems. Currently, the predictive mean residence time relies on an empirical entrainment coefficient with a range in variance due to the absence of hydraulic and geomorphic quantities driving mass exchange. Two empirically derived relationships are presented for the mean residence time of lateral cavities-a prevalent and widely recognized type of transient storage-in gravel-bed rivers and streams that incorporates hydraulic and geomorphic parameters. The relationships are applicable for gravel-bed rivers and streams with a range of cavity width to length (W/L) aspect ratios (0.2-0.75), shape, and Reynolds numbers (Re, ranging from 1.0 x 10(4) to 1.0 x 10(7)). The relationships equate normalized mean residence time to nondimensional quantities: Froude number, Re, W/L, depth ratio (ratio of cavity to shear layer depth), roughness factor (ratio of shear to channel velocity), and shape factor (representing degree of cavity equidimensionality). One relationship excludes bed roughness (equation (13)) and the other includes bed roughness (equation (14)). The empirically derived relationships have been verified for conservative tracers (R-2 of 0.83) within a range of flow and geometry conditions. Topics warranting future research are testing the empirical relationship that includes the roughness factor using parameters measured in the vicinity of the cavity to reduce the variance in the correlation, and further development of the relationship for nonconservative transport.