Surface velocity divergence model of air/water interfacial gas transfer in open-channel flows

Abstract

Air/water interfacial gas transfer through a free surface plays a significant role in preserving and restoring water quality in creeks and rivers. However, direct measurements of the gas transfer velocity and reaeration coefficient are still difficult, and therefore a reliable prediction model needs to be developed. Varying systematically the bulk-mean velocity and water depth, laboratory flume experiments were conducted and we measured surface velocities and dissolved oxygen (DO) concentrations in open-channel flows to reveal the relationship between DO transfer velocity and surface divergence (SD). Horizontal particle image velocimetry measurements provide the time-variations of surface velocity divergence. Positive and negative regions of surface velocity divergence are transferred downstream in time, as occurs in boil phenomenon on natural river free-surfaces. The result implies that interfacial gas transfer is related to bottom-situated turbulence motion and vertical mass transfer. The original SD model focuses mainly on small-scale viscous motion, and this model strongly depends on the water depth. Therefore, we modify the SD model theoretically to accommodate the effects of the water depth on gas transfer, introducing a non-dimensional parameter that includes contributions of depth-scale large-vortex motion, such as secondary currents, to surface renewal events related to DO transport. The modified SD model proved effective and reasonable without any dependence on the bulk mean velocity and water depth, and has a larger coefficient of determination than the original SD model. Furthermore, modeling of friction velocity with the Reynolds number improves the practicality of a new formula that is expected to be used in studies of natural rivers.