Heat flux through a geothermally heated fluidized bed at the bottom of a lake

摘要

Heat fluxes and the underground inflow through a natural fluidized bed within the main sub-basin of Lake Banyoles are studied and parameterized. In the upper part of this fluidized bed, at a depth of about 30 m, the vertical gradients of particle concentration and temperature are very sharply located within an interface a few centimeters thick. Within this interface (lutocline), the depths where the temperature and the concentration gradients are maximum match exactly. On the other hand, the lutocline determines a flat, horizontal surface dividing the water column into a hot, turbid medium at the bottom and clear, colder, bulk water above. Through this interface the flow regime also varies from being laminar just below it, to turbulent due to convective processes developing above it. More precisely, in studied main sub-basin a buoyant plume develops above the lutocline, as a result of the heat flux, and affects the lake's water quality due to particles dragged along by it. In this paper it is proposed to determine the temperature at the depth of maximum gradient within the interface by means of measured temperature profiles, and consider the stationary heat transport equation in the laminar region below it, in order to obtain the water velocity and the heat flux. Heat flux parameterization is given based on a large number of thermal high-resolution profiles, covering six campaigns in different years and seasons. Furthermore, and in consideration of the fact that high-resolution thermal profiles are not always available, some alternative parameterizations for the heat flux are presented based only on the temperature of the fluidized bed and that of the lower hypolimnion.