Conductive and convective heat transfer in sediments near streams

Abstract

An Fourier Series solution is presented that describes the simultaneous, one-dimensional, vertical flow of heat and ground water in homogeneous, porous media beneath streams. Use of this analytical solution provides an indirect method of determining vertical flow rates and the effective vertical hydraulic connection between sediments and overlying streams. The method consists of varying the Darcy velocity in the solution until the temperature profiles predicted by the solution match those measured in the field. The method was applied at three field sites in Central Massachusetts. At the first site, which is underlain by lacustrine clay, the vertical flow rate through the clay was determined to be less than 5x10⁻⁷ cm/s and the vertical hydraulic conductivity was less than 0.08 cm/s. The vertical flow rate through mixed sand and gravel underlying the second site equaled 7.5x10⁻⁶ cm/s and vertical hydraulic conductivities of sediments underlying the site ranged from 3.8x10⁻⁴ to 3.1x10⁻³ cm/s. The vertical flow rate through mixed sand and gravel underlying the third site ranged from 3x10⁻⁵ to 7x10⁻⁵ cm/s and vertical hydraulic conductivities of sediments underlying the site ranged from 1x10⁻³ to 4x10⁻³ cm/s. The simultaneous flow of heat and ground water in sediments beneath streams may be more complex than that assumed for the Fourier Series solution. The additional complexity may be partially attributable to two factors: the presence of horizontal ground-water flow, and the presence of thermal conditions near the stream that differ from conditions in the stream itself. The effects of that these two factors have on thermal regimes in sediments beneath streams were investigated using numerical simulations. Results indicate, for example, that under conditions of no horizontal ground-water flow, thermal conditions near the stream can affect temperatures in sediments beneath the stream as far as 900 cm from the stream bank. For horizontal flow rates greater than about 1x10⁻⁴ cm/s, thermal conditions near the stream can affect temperatures in sediments beneath the stream as far as 1500 cm from the stream bank. The method of determining flow rates and hydraulic connection has been applied to stream-aquifer systems. However, the method also may have application in other hydrologic settings. Two such applications might be to determine flow rates to and from lakes and rates of recharge to aquifers.