Wind-driven mixing in near-shore lake environments: Application to phosphorus dynamics

A one-dimensional modeling framework is developed to serve as an analytical tool to evaluate phosphorus fate and transport in the nearshore regions of large lakes, in particular the Great Lakes of North America. The model incorporates phosphorus loading, filtering at the bottom of the water column by (invasive) mussels, uptake by benthic algae, and vertical transport. A critical component of the model is the specification of vertical diffusivity as a function of wind speed, and various approaches to determine vertical diffusivity as a function of depth are investigated. A modified version of a wave-orbital velocity model is developed and proposed for this purpose. The model results are compared with calibrated diffusivities obtained in a field study in Good Harbor Bay, Lake Michigan. It is further shown that, even in a relatively shallow environment, depth-dependency is an important factor in modeling vertical concentration profiles. Although the study is motivated by the need to develop analysis tools to evaluate different aspects of the so-called "nearshore shunt" hypothesis relating phosphorus distributions with benthic algae and mussels, the model developed here may serve in a more general sense as a framework for predicting the vertical distribution of any contaminant in the nearshore zone of a large lake.