Model for Wind-Driven Vertical Mixing in a Shallow Lake with Submersed Macrophytes

An energy flux model to simulate vertical mixing in a temperature stratified shallow lake with submersed macrophytes has been formulated. The model is based on a one-dimensional equation for transport and dissipation of kinetic energy produced by wind, coupled to heating at the water surface. Analytic solutions of the energy flux equation characterize the steady-state mixed layer depth for constant wind shear and constant heat input at the water surface. It is found that in water columns with sparse macrophytes, the mixed layer depth is controlled by the buoyancy length scale, which is proportional to the heat flux. In dense macrophyte beds, the mixed layer depth is controlled primarily by the macrophyte length scale, which is a function of the plant surface area. The analytic steady-state solutions give a lower bound for daytime mixed layer depth, which is controlled by simultaneous heating and wind mixing from the water surface.