Verifying Lake Transport Models with Spectral Statistics

A sequence of numerical experiments is performed to determine the suitability of coarse grid lake turbulence models developed in the accompanying paper in perserving theoretically known variance spectra. A complete review of theoretically known variance spectra is presented and all relevant spectral data from aquatic field experiments is summarized. Three basins are used and set into motion by a spectrally correct Markov model wind shear. Wave number spectra were calculated by Taylor's hypothesis from time series collected at the basin center. Based on these numerical experiments it is concluded that low pass filter preparation is a necessity for coarse grid spectra preservation. Traditional model formulations will not reproduce the known spectra. Experiments revealed that the hydrostatic pressure assumption and rigid lid pressure formulation only permit a two dimensional turbulence structure which is, of course, not observed in field data except during fluid acceleration.