A Simplified Parametric Model for Fetch-Limited Peak Wave Frequency in Shallow Estuaries

A study was conducted on the wave energy and peak wave frequency in Breton Sound, Louisiana. A bottom-mounted Acoustic Doppler Velocimeter was used to measure waves and currents. The results of the study indicate that the asymptotic limits for the wave energy and peak wave frequency can be defined accurately, while the integral properties of the wave field estimated by the existing parametric wave models, particularly the peak wave frequency, suffer from a lack of accuracy. Based on the observed dependency of peak frequency on the ratio of wind fetch to water depth, a simplified parametric model is proposed in an effort to increase the accuracy of the estimated peak wave frequency. The physical boundaries between water depth and wind fetch for proper estimation of the peak frequency are introduced. The model was evaluated for the goodness of fit against measured data that had been collected at a different study site. The proposed model proved to be more accurate in comparison to previous methods. Further assessment of the new relationship, along with the measured data, revealed that water depth had a more significant effect on the peak wave frequency in the fetch-limited shallow water than did wind fetch. The simplicity of the proposed model, with fewer unknown coefficients compared to other existing models, makes it convenient for practical applications and requires less effort to be calibrated for shallow estuaries of differing bottom roughness.