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 discharge flow driven by cooling or destabilising forcing at the water surface in a water body with variable 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 essentially flat bottomed interior, as well as published results from the literature. The steady state horizontal 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.

Horizontal exchange flows driven by spatial variation of buoyancy fluxes through the water surface are found in a variety of geophysical situations. In all examples of such flows the timescale characterizing the variability of the buoyancy fluxes is important and it can vary greatly in magnitude. In this laboratory study we focus on the effects of this unsteadiness of the buoyancy forcing and its influence on the resulting flushing and circulation processes in a cavity. The experiments described all start with destabilizing forcing of the flows, but the buoyancy fluxes are switched to stabilizing forcing at three different times spanning the major timescales characterizing the resulting cavity-scale flows. For destabilizing forcing, these timescales are the flushing time of the region of forcing, and the filling-box timescale, the time for the cavity-scale flow to reach steady state. When the forcing is stabilizing, the major timescale is the time for the fluid in the exchange flow to pass once through the forcing boundary layer. This too is a measure of the time to reach steady state, but it is generally distinct from the filling-box time. When a switch is made from destabilizing to stabilizing buoyancy flux, inertia is important and affects the approach to steady state of the subsequent flow. Velocities of the discharges from the end regions, whether forced in destabilizing or stabilizing ways, scaled as u∼(Bl)1/3 (where B is the forcing buoyancy flux and l is the length of the forcing region) in accordance with Phillips' (1966) results. Discharges with destabilizing and stabilizing forcing were, respectively, Q−∼(Bl)1/3H and Q+∼(Bl)1/3δ (where H is the depth below or above the forcing plate and δ is the boundary layer thickness). Thus Q−/Q+>O(1) provided H>O(δ), as was certainly the case in the experiments reported, demonstrating the overall importance of the flushing processes occurring during periods of cooling or destabilizing forcing.

Many wetlands around the world are characterized by shallow water, dense vegetation in the littoral zones, no significant riverine inflow and minimal circulation. Recent research on the hydrodynamics of such wetlands has identified convective circulation as being important for flushing of the littoral zones. To quantify this process, a parameterization of the convective discharge per unit width, which had been previously developed for nonvegetated systems, was extended to include a drag coefficient dependent on Reynolds number and vegetation density. The drag coefficient also included the effect of anisotropic permeability of the vegetation. The effects of relatively dense emergent vegetation (ϳ17% by volume) on convective flushing of shallow wetlands with low-Reynolds number (ϳ100) flow was then investigated using experiments in a laboratory convection tank (0.5 by 2 by 0.1 m) and in a wetland mesocosm (5 by 15 by 1 m). Bottom convective currents of ϳ1-10 mm s Ϫ1 were measured in both the laboratory and the mesocosm. These currents resulted in the shallow, vegetated regions of the mesocosm being flushed in 4 h. The discharge per unit width (m 2 s Ϫ1 ) predicted by the developed parameterization compared favorably (R 2 ϭ 0.7) with the discharge per unit width measured in both the laboratory and the mesocosm. The short timescales of convective flushing, even in the presence of reasonably dense vegetation, indicate the likely significance of this mechanism in sheltered wetlands.Convective circulation occurs in aquatic systems when shallow waters heat or cool more rapidly than deeper waters, causing horizontal gradients in water temperature and density. The horizontal density differences drive convective currents, which allow increased flushing of the littoral regions. In wetlands, these littoral zones are typically characterized by dense emergent vegetation, yet the effect of vegetation on convective circulation has rarely been addressed. This paper develops parameterizations to describe that effect, then presents some preliminary laboratory and field data to test the parameterization.Convective currents have been frequently observed in deep lakes (e.g., Monismith et al. 1990;Nepf and Oldham 1997), and they have also been measured in shallow wetlands. Arnold and Oldham (1997) measured the distinctive signals of cool convective currents inserting along the bottom boundary of a shallow (2 m deep) wetland (Fig. 1) for Ͼ30% of the year. These bottom currents are typically 0 (1-10) mm s Ϫ1 (Sturman et al. 1999). Although this is low compared to currents measured in lakes dominated by river in-1

Convection driven by spatially variable heat transfer across the water surface is an important transport mechanism in many geophysical applications. This flow is modelled in a rectangular tank with an aspect ratio, H/L, of 0.1 (where H and L are the tank height and length, respectively). Heat fluxes are applied through horizontal copper plates of length 0.1 L located at the top of one end of the tank and at the bottom of the other end. Experimental flows have been forced with heating at the bottom of the tank and cooling at the top, which gives rise to unstable convection in the end regions. Using water and a glycerol/water mix as the experimental fluids, flow visualization studies and measurements of temperature, velocity and heat flux have been made. Flow visualization studies revealed that complex unsteady turbulent flows occupied the end regions, while cubic velocity profiles characterized the horizontal laminar flow in the interior of the tank. Simple scaling arguments were developed for steady-state velocity and temperature fields, which are in good agreement with the experimental data. In the current experiments the portion of the plates closest to the tank interior (and to the tank endwall in the case of the glycerol/water experiments) were occupied by laminar boundary layers, while the remainder of the plates were occupied by turbulent flow. An effective Rayleigh number Ra* was defined, based upon the portion of the plate occupied by turbulent flow, as was a corresponding modified Nusselt number Nu*. The heat transfer was well predicted by classical Rayleigh-Bénard scaling with the Nusselt number Nu* ∼ Ra*1/3. The range of Ra* was 4.3 × 105 ≤ Ra* ≤ 1.7 × 108. Scaling arguments predicted the triple occupancy of the plates by differing boundary layer regimes within the range of 105 ≤ Ra* ≤ 1014.

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