Thermal wave dynamics in rivers affected by hydropeaking

Release of water from reservoirs for hydropower production generates intermittent hydropeaking and thermopeaking waves in receiving rivers that can have important ecological implications at a variety of time and spatial scales. In this paper a coupled analytical-numerical approach is used in order to grasp the relevant processes of the propagation of the hydrodynamic and thermal waves, within the framework of a one-dimensional mathematical model governed by the Saint Venant equations coupled with a thermal energy equation. While interacting with external forcing, the waves propagate downstream with different celerities such that it is possible to identify a first phase of mutual overlap and a second phase in which the two waves proceed separately. A simplified analytical solution for flow depth and temperature is derived in explicit terms, exploiting the typical square shape of the waves and transforming the boundary conditions into equivalent initial conditions. The numerical model, which retains the complete features of the problem, is solved using a second order finite volume method. The wave properties and the characteristic timescales are investigated by means of the analytical solution and compared with numerical results for some test cases. Overall, the present approach allows for a deeper insight into the complex dynamics that characterize the propagation of hydropeaking and thermopeaking waves.