Steady convective exchange flows down slopes Jeff J. Sturman, Carolyn E. Oldham * and Greg N. Ivey Centre for Water Research and Department of Environmental Engineering, University of Western Australia, Nedlands, Western Australia, 6907, Australia, e-mail: oldham@cwr.uwa.edu.au Key words: Hydrodynamics, limnology, destabilising, convection, slopes, pollutants. ABSTRACT Horizontal exchange flows driven by destabilising buoyancy fluxes through the surface waters of lakes and coastal regions of oceans are important in understanding the transport of nutrients, micro-organisms and pollutants from littoral to pelagic zones. Our interest here is in the dischar- ge flow driven by cooling or destabilising forcing at the water surface in a water body with varia- ble depth due to sloping bottom topography. Flow visualisation studies and measurements in a laboratory model enabled us to develop scaling arguments to predict the dependency of discharge upon surface forcing and the angle of bottom slope. The results were used to interpret both the laboratory measurements and field data from a small shallow lake with sloping sides and an essen- tially flat bottomed interior, as well as published results from the literature. The steady state hori- zontal exchange can be described by Q = 0.24 B 1/3 (l tan q/(1 + tan q)) 4/3 , where Q is the discharge rate per unit length of shoreline, q is the angle of the bottom slope, B is the surface buoyancy flux and l is the horizontal length of the forcing region over the slope. The flushing timescale of the wedge shaped littoral region was given by t f ~l 2/3 (1 + tan q) 4/3 /(B tan q) 1/3 . While the buoyancy flux in the field is almost never constant in space or time and the slope from the shore is seldom uniform, we found that the exchange rate was relatively insensitive to buoyancy flux changes and only moderately sensitive to slope. 1. Introduction This work is motivated by an interest in convectively driven horizontal exchange flows in the side-arms and shallow littoral regions of lakes, semi-enclosed seas and coastal ocean environments. Such flows are driven by spatial and temporal variation of buoyancy fluxes through the water surface and are affected by sloping bottom topography. We deal mainly with the steady state condition, although unsteady forcing can be an important feature of the field situation (e. g., Farrow and Patter- son, 1993; Horsch et al., 1994; Sturman and Ivey, 1998). Exchange flows in side-arms have been modelled using a variety of topographi- cal assumptions and forcing arrangements. Early modelling of convectively driven Aquat.sci.61 (1999) 260 – 278 1015-1621/99/030260-19 $ 1.50+0.20/0 © Birkhäuser Verlag, Basel, 1999 Aquatic Sciences * Author for correspondence.