Synopsis of Analytic Solutions for the Temperature Distribution in a River Downstream from a Dam or Reservoir

摘要

A synopsis of analytic solutions for river temperature downstream from a dam is presented. Transient, convective, and diffusive effects are considered as well as periodic and spatially varying surface heat exchange. Two new solutions of the transient equation for heat transport in a river with fluctuating surface heat exchange have been developed. The first describes the transient-convective temperature response in a river subjected to ta combination of fluctuating and spatially varying surface heat transfer. The second new solution represents a complete transient-convective-diffusive solution to the equation for river temperature when surface heat exchange is dependent upon periodically varying meteorological conditions. The parameters determining the amplitude of the river response, as well as the lag between atmospheric forcing and river response, are delineated.