The impact of boat traffic on the health of coastal ecosystems is a multi-scale process: from minutes (individual wakes) to days (tidal modulation of sediment transport), to seasons and years (traffic is seasonal). A considerable numerical effort, notwithstanding the value of a boat-by-boat numerical modeling approach, is questionable, because of the practical impossibility of specifying the exact type and navigation characteristics for every boat comprising the traffic at any given time. Here, we propose a statistical-mechanics description of the traffic using a joint probability density of the wake population in some characteristic parameter space. We attempt to answer two basic questions: (1) what is the relevant parameter space and (2) how should a numerical model be tested for a wake population? We describe the linear and nonlinear characteristics of wakes observed in the Florida Intracoastal Waters. Adopting provisionally a two-dimensional parameter space (depth- and length-based Froude numbers) we conduct numerical simulations using the open-source FUNWAVE-TVD Boussinesq model. The model performance is excellent for weakly-dispersive, completely specified wakes (e.g., the analytical linear wakes), and also for the range of Froude numbers observed in the field, or for large container ships generating relatively long waves. The model is challenged by the short waves generated by small, slow boats. However, simulations suggest that the problem is confined to the deeper water domain and linear evolution. Nonlinear wake shoaling, essential for modeling wake-induced sediment transport and wake impact on the environment, is described well.
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