Refraction of Wind-Wave Spectra in shallow waters: 
Applications to the Coast of Sao Francisco do Sul, SC, Brazil.

Jose Henrique G. M. Alves

Thesis submitted to the Environmental Engineering Post-Graduate Program of the Santa Catarina Federal University in the fulfillment of the requirements for the degree of Master of Science in Environmental Engineering. Florianopolis, SC, Brazil, 1996.


A methodology for studying wave spectrum transformation in shallow waters is proposed and applied considering several wave conditions measured at the coast of Sao Francisco do Sul, a northern coastal locality of the Santa Catarina State, Southern Brazil. The methodology includes deep water spectrum estimation using wave measurements from a single shallow water site and the reconstitution of the complete wave field at several points near the coastal region. Results from directional measurements of the wave field are used to determine the summer and autumn wave climate at the study site. Four dominat wave climate patterns are identified and related back to meteorological scenery. Governing functions of the wave transformation along the coastal region are determined through the application of a back-refraction numerical model. Two methodologies for determining the directional energy distribution are tested and compared. The maximum entropy method shows best results than standard parametrisation and is used to determine measured shallow water spectra. Through back-refraction, the inverse direction and energy transfer functions are calculated to determine deep water directional spectra. The computations show that refraction attenuates energy transported by the waves from deep water to the measuring point. A "progressive" spectral refraction model is developed and used to recover the wave field at an extensive coastal area nearby the measuring point. Numerically simulated significant wave height and directional spectra are compared to the original data. The very good agreement shows that the application of the proposed methodology provides reliable results regarding the study site.

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