Depth-Dependent Dispersion Coefficient for Modeling of Vertical Solute Exchange in a Lake Bed under Surface Waves Qin Qian 1 ; Jeffrey J. Clark 2 ; Vaughan R. Voller 3 ; and Heinz G. Stefan 4 Abstract: Variable pressure at the sediment/water interface due to surface water waves can drive advective flows into or out of the lake bed, thereby enhancing solute transfer between lake water and pore water in the lake bed. To quantify this advective transfer, the two-dimensional 2D advection-dispersion equation in a lake bed has been solved with spatially and temporally variable pressure at the bed surface. This problem scales with two dimensionless parameters: a “dimensionless wave speed” W and a “relative dispersivity” . Solutions of the 2D problem were used to determine a depth-dependent “vertically enhanced dispersion coefficient” D E  that can be used in a 1D pore-water quality model which in turn can be easily coupled with a lake water quality model. Results of this study include a relationship between D E and the depth below the bed surface for W  50 and  0.1. The computational results are compared and validated against a set of laboratory measurements. An application shows that surface waves may increase the sediment oxygen uptake rate in a lake by two orders of magnitude. DOI: 10.1061/ASCE0733-94292009135:3187 CE Database subject headings: Dispersion; Lakes; Mass transfer; Hydraulic models; Sediment; Solutes; Surface wave; Water quality. Introduction Water motion in a lake can have profound consequences for its ecosystem. Periodic surface waves induced by wind are among the important water movements in lakes Horne and Goldman 1994. Wind induced surface waves cause water pressure fluctua- tions at the lake bed which, in turn, affect pore pressures and can cause flow into and out of a porous lake bed. Similarly small bed forms over which a benthic current is flowing, induce pressure variations along the sediment surface as described by Huettel and Rusch 2000 for small mound and ripples on shelf sediments, and by Elliot and Brooks 1997 for dunes in streams. The pressure-driven advection of water into and out of the pore system of a lake bed can enhance the transfer of a dissolved substance solute significantly. Wave-induced advective flow in permeable sediments has been described by Huettel and Webster 2001, Chapter 7. Studies of pore-water advection have been conducted in marine environments. Shum and Sundby 1996 and Jahnke et al. 2005 estimated the effect of advection on organic matter processing in continental shelf sediments. Van Rees et al. 1996 indicated that, in addition to particle size, benthic organ- isms also affect the solute transport in lake sediments. Huettel and Rusch 2000 found that the advective transport, associated with small mounds and ripples commonly found on shelf sediments, increased penetration depth of unicellular algae into sandy sedi- ment up to a factor of seven and mass flux up to a factor of nine compared to a smooth sediment surface. Experiments on an inter- tidal sand flat Rusch and Huettel 2000 demonstrated that advec- tive particle transport into permeable sediments depends on sediment permeability and particle size. Surface gravity waves can increase fluid exchange between sandy sediment and overly- ing shallow water 50-fold, relative to exchange by molecular dif- fusion Precht and Huettel 2003. Precht et al. 2004 studied the effects of advective pore-water exchange driven by shallow water waves on the oxygen distribution in permeable natural sediment in a wave tank. The strong and relatively recent evidence of advective interac- tion between the surface water and the pore water, especially if the lake sediment is highly permeable, calls into question the often used model that molecular diffusion is the dominant solute transport process at the sediment/water interface Glud et al. 1996. The objective of this paper is to quantify the advective pore-water flow due to a progressive moving sinusoidal pressure wave on a lake bed and its effect on solute transport in lacustrine sediments. The analysis will be 2D, but a 1D vertical, depth- dependent “enhanced dispersion coefficient D E ,” which ac- counts for both advection and hydrodynamic dispersion tensors in the permeable lake bed, will be related quantitatively to pressure wave amplitude a, wavelength L, wave speed c, bed hydrau- lic conductivity K, and depth below the lake bed/water interface y. The enhanced dispersion coefficient D E  can be used in a 1D vertical dispersion equation which can also incorporate chemi- 1 Ph.D. Candidate, St. Anthony Falls Laboratory, Dept. of Civil Engi- neering, Univ. of Minnesota, Minneapolis, MN 55414; presently, Assis- tant Professor, Dept. of Civil Engineering, Lamar Univ., Beaumont, TX 77710 corresponding author. E-mail: qian0037@umn.edu 2 Associate Professor, Geology Dept., Lawrence Univ., Appleton, WI 54912. 3 Professor, St. Anthony Falls Laboratory, Dept. of Civil Engineering, Univ. of Minnesota, Minneapolis, MN 55414. 4 Professor, St. Anthony Falls Laboratory, Dept. of Civil Engineering, Univ. of Minnesota, Minneapolis, MN 55414. Note. Discussion open until August 1, 2009. Separate discussions must be submitted for individual papers. The manuscript for this paper was submitted for review and possible publication on October 21, 2007; approved on August 11, 2008. This paper is part of the Journal of Hy- draulic Engineering, Vol. 135, No. 3, March 1, 2009. ©ASCE, ISSN 0733-9429/2009/3-187–197/$25.00. JOURNAL OF HYDRAULIC ENGINEERING © ASCE / MARCH 2009 / 187 Downloaded 17 Feb 2010 to 128.101.188.45. Redistribution subject to ASCE license or copyright; see http://pubs.asce.org/copyright