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Abstract(s)
Este trabalho apresenta uma análise das características não lineares e não estacionárias associadas à hidrodinâmica de ondas em zonas costeiras, objetivando verificar o potencial que metodologias recentes possuem para identificar tais aspectos que são excluídos das hipóteses de dedução das metodologias usuais conhecidas como a Transformada de Fourier e da Teoria Linear das Ondas. No decorrer do texto, são discutidas as considerações teóricas pertinentes ao assunto, associando as assimetrias a definição dos elementos de onda, aos fenômenos presentes na Zona de Transformação das Ondas e ao transporte de sedimentos. A análise é realizada sob dois aspectos. O primeiro, refere-se a análise espectral onde são aplicadas três Transformadas: a de Fourier, por Ôndulas e a de Hilbert-Huang. O segundo, baseia-se na aplicação de um conjunto de parâmetros matemáticos representativos das magnitudes e assimetrias das ondas, capaz de descrever a hidrodinâmica costeira, proposto por Abreu et al. (2011). Para o efeito, as potencialidades destes métodos são exploradas através da sua aplicação a séries temporais da elevação da superfície livre obtidas através de oito sensores de pressão colocados numa campanha de campo realizada na praia de São Jacinto, Portugal, em Junho de 2015. Os resultados apresentados pelos espectros de Ôndulas e de Hilbert-Huang foram satisfatórios e complementares, sendo capazes de representar as variações das frequências durante o tempo (a nível de não linearidades e de não estacionariedades), uma lacuna deixada pelo Espectro de Fourier. Os parâmetros matemáticos identificaram, para diferentes profundidades, as assimetrias das ondas, permitindo a caracterização dos perfis das ondas para cada variação de maré observada, corroborando com os resultados esperados para ondas incidentes nas Zonas de Transformação e Arrebentação. Foram ainda obtidos os resultados da Altura Significativa da Onda e do Período de Pico, validando a comparação com dados da Boia ondógrafo de Leixões. Em função da localização dos oito sensores na praia, foi possível estudar, usando diferentes filtros de processamento do sinal, o comportamento assimétrico das ondas e demonstrar o aumento das características não lineares conforme as ondas ao largo se propagam para águas rasas.
This thesis presents an analysis of non-linear and non-stationary characteristics associated with waves’ hydrodynamics in coastal zones, with the objective of verifying the potential that recent methodologies have in identifying the aspects that are excluded from the deduction hypothesis of the more usual Fourier Transform and Linear Wave Theory methodologies. Along the text, theoretical considerations regarding the subject are discussed, associating the asymmetries to wave elements definition, the phenomena present at the Wave Transformation Zone, and to sediment transport. The analysis is done under two aspects. The first being the spectral analysis where three Transforms are applied: Fourier’s, Wavelet, and Hilbert-Huang. The second aspect is based on the application of Abreu et al. (2011) proposed set of mathematical parameters that represent the magnitude and asymmetries of waves, capable of describing coastal hydrodynamics. In order to do this, the potential of these methodologies are explored by applying them to timed series of free surface elevations obtained from eight pressure sensors placed on a field campaign at the beach of São Jacinto, Portugal, on June 2015. The results presented by the Wavelet and Hilbert-Huang spectra were satisfactory and complemented each other, being able to represent the frequency variations during time (non-stationarity), a gap that was left by the Fourier Transform. The mathematical parameters identified, for different depths, the waves’s asymmetries, enabling wave profile characterization for each observed tide variation, supporting the results that were expected at the Transformation and Surf zones. The results for significant wave height and peak period were also obtained, validating the data comparison with Leixões’ directional wave buoy. Due to the location of the eight pressure sensors at the beach, it was possible to study the asymmetrical wave behaviors, using different signal processing filters, and to demonstrate the increase of nonlinearity as longshore waves transform into nearshore waves.
This thesis presents an analysis of non-linear and non-stationary characteristics associated with waves’ hydrodynamics in coastal zones, with the objective of verifying the potential that recent methodologies have in identifying the aspects that are excluded from the deduction hypothesis of the more usual Fourier Transform and Linear Wave Theory methodologies. Along the text, theoretical considerations regarding the subject are discussed, associating the asymmetries to wave elements definition, the phenomena present at the Wave Transformation Zone, and to sediment transport. The analysis is done under two aspects. The first being the spectral analysis where three Transforms are applied: Fourier’s, Wavelet, and Hilbert-Huang. The second aspect is based on the application of Abreu et al. (2011) proposed set of mathematical parameters that represent the magnitude and asymmetries of waves, capable of describing coastal hydrodynamics. In order to do this, the potential of these methodologies are explored by applying them to timed series of free surface elevations obtained from eight pressure sensors placed on a field campaign at the beach of São Jacinto, Portugal, on June 2015. The results presented by the Wavelet and Hilbert-Huang spectra were satisfactory and complemented each other, being able to represent the frequency variations during time (non-stationarity), a gap that was left by the Fourier Transform. The mathematical parameters identified, for different depths, the waves’s asymmetries, enabling wave profile characterization for each observed tide variation, supporting the results that were expected at the Transformation and Surf zones. The results for significant wave height and peak period were also obtained, validating the data comparison with Leixões’ directional wave buoy. Due to the location of the eight pressure sensors at the beach, it was possible to study the asymmetrical wave behaviors, using different signal processing filters, and to demonstrate the increase of nonlinearity as longshore waves transform into nearshore waves.
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Keywords
Transformada por Ôndulas Transformada de Hilbert-Huang Transformada de Fourier Ondas assimétricas Filtros Wavelet Transform Hilbert-Huang Transform Fourier Transform Asymmetrical waves Filters