Steady convective exchange flows down slopes

Horizontal exchange flows driven by destabilising buoyancy fluxes through t he surface waters of lakes and coastal regions of oceans are important in u nderstanding the transport of nutrients, micro-organisms and pollutants fro m littoral to pelagic zones. Our interest here is in the discharge flow dri ven by cooling or destabilising forcing at the water surface in a water bod y with variable depth due to sloping bottom topography. Flow visualisation studies and measurements in a laboratory model enabled us to develop scalin g arguments to predict the dependency of discharge upon surface forcing and the angle of bottom slope. The results were used to interpret both the lab oratory measurements and field data from a small shallow lake with sloping sides and an essentially flat bottomed interior, as well as published resul ts from the literature. The steady state horizontal exchange can be describ ed by Q = 0.24 B-1/3 (l tan theta/(1 + tan theta))(4/3), where Q is the dis charge rate per unit length of shoreline, a is the angle of the bottom slop e, B is the surface buoyancy nux and I is the horizontal length of the forc ing region over the slope. The flushing timescale of the wedge shaped litto ral region was given by tau(i) similar to l(2/3) (1 + tan theta)(4/3)/(B ta n theta)(1/3). While the buoyancy flux in the field is almost never constan t 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.