Analytical Solutions for Open Channel Temperature Response to Unsteady Thermal Discharge and Boundary Heating

摘要

Analytical solutions are derived for a one-dimensional model of the bulk temperature response of open-channel flow with unsteady and nonuniform heating at an upstream boundary, the water surface, and the riverbed. The model describes the temperature variation as kinematic waves, and the solutions are explicit formulas that are comprised of transient terms, which play dominant roles at the upstream end, and equilibrium terms, which determine the temperature far downstream. It is shown that the time-dependence of the solutions includes solution envelopes that can be both complex as well as interesting because of the interplay between the upstream and lateral boundary conditions. The applicability of the solutions to practical problems is demonstrated for two cases: (1) a stream bounded at its upstream end by a dam and with a mid-reach inflow that is also subject to diurnal heating; and (2) Boulder Creek, Colorado, which is impacted by effluent released from a waste water treatment plant. The model prediction is in reasonable agreement with gauged data.