An Energy Based Model for Coastal Bays and Lakes

by William S. Appleton, Purdue Univ, West Lafayette, United States,
William L. Wood, Purdue Univ, West Lafayette, United States,
Yan-Sheng Chang, Purdue Univ, West Lafayette, United States,

Document Type: Proceeding Paper

Part of: Estuarine and Coastal Modeling


The North American Great Lakes have numerous tributary bays and small lakes along their coastline that open directly to the Great Lakes through natural or engineered channels. As a consequence of these direct channel connections, significant free surface resonant motions are produced within these bodies by transmitted wave energy from Great Lakes storms. A conservation of energy approach is applied to develop a linear, inviscid, dispersive, hybrid finite element resonance model for calculating free surface wave response in an adjoining coastal basin of arbitrary shape. The governing model equation is based on the mild slope wave equation and includes wave refraction, diffraction, and reflection applied to both long and short waves. The functional is constructed to also incorporate variable bathymetry, bottom friction and variable, full or partial absorbing boundaries. A scheme was developed which incorporates the determination of absorption coefficients into the model as a function of incident wave height, wave length, boundary type and slope. A detailed numerical model of Lake Macatawa, an adjacent lake connected directly to Lake Michigan, has been developed and sensitivity testing performed. Preliminary model results compare favorably with field observations.

Subject Headings: Surface waves | Lakes | Wave equations | Water waves | Resonance | Mathematical models | Free surfaces | Great Lakes | Lake Michigan

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