VESSEL WAVE WAKE CHARACTERISATION USING WAVELET ANALYSIS

This work focuses on characterising vessel wave wake (wash) using wavelet analysis when a vessel is operating in the sub-critical and critical zone. Such characterisation complements other wash characteristics: Froude depth number, bow wave angle, solitons and decay coefficient. The examination of experimental results indicates that differences in characteristics with respect to water depth, Froude depth number, vessel displacement, hull form and soliton generation can be identified through wavelet analysis. The results demonstrate “proof of concept” that wavelet analysis is a powerful tool for characterising vessel wash and captures the effects of key operational and vessel changes.

The existence of time-dependent attractor for wave equation with fractional damping and lower regular forcing term

<p style='text-indent:20px;'>We investigate the well-posedness and longtime dynamics of fractional damping wave equation whose coefficient <inline-formula><tex-math id="M1">\begin{document}$ \varepsilon $\end{document}</tex-math></inline-formula> depends explicitly on time. First of all, when <inline-formula><tex-math id="M2">\begin{document}$ 1\leq p\leq p^{\ast\ast} = \frac{N+2}{N-2}\; (N\geq3) $\end{document}</tex-math></inline-formula>, we obtain existence of solution for the fractional damping wave equation with time-dependent decay coefficient in <inline-formula><tex-math id="M3">\begin{document}$ H_{0}^{1}(\Omega)\times L^{2}(\Omega) $\end{document}</tex-math></inline-formula>. Furthermore, when <inline-formula><tex-math id="M4">\begin{document}$ 1\leq p&lt;p^{*} = \frac{N+4\alpha}{N-2} $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M5">\begin{document}$ u_{t} $\end{document}</tex-math></inline-formula> is proved to be of higher regularity in <inline-formula><tex-math id="M6">\begin{document}$ H^{1-\alpha}\; (t&gt;\tau) $\end{document}</tex-math></inline-formula> and show that the solution is quasi-stable in weaker space <inline-formula><tex-math id="M7">\begin{document}$ H^{1-\alpha}\times H^{-\alpha} $\end{document}</tex-math></inline-formula>. Finally, we get the existence and regularity of time-dependent attractor.</p>

Numerical modelling of FC bacteria using a dynamic and variable mortality rate

Faecal coliform (FC) microorganisms are one of the most important indicators in water quality management, since their presence reveals the possibility of existence of other dangerous microorganisms, leading to higher health risks. An accurate estimate of the concentration of this indicator helps better evaluation of the water pollution in riverine basins; thus, it is essential for future developments. The FC mortality rate depends on the physical, chemical, and biological processes in rivers. These processes are generally affected by environmental conditions. In this study, the decay coefficient (K) or mortality rate are related to the environmental parameters such as temperature, turbidity, pH, and salinity by an empirical equation. The results showed that turbidity and temperature are the most effective parameters. Moreover, an empirical equation was developed utilizing numerical model calibration, which describes the relationship of the mortality rate (K) with water temperature and turbidity. This equation was then added to the water quality module of the FASTER numerical model. Comparison of the measured FC concentrations with the predicted values obtained from the numerical model showed that the model accuracy significantly improved for the dynamic and variable decay coefficient.

Modelagem simplificada do fósforo total em lagos e reservatórios brasileiros

Resumo O fósforo é considerado o principal fator responsável pela eutrofização de lagos e reservatórios. No presente estudo, utilizou-se um modelo transiente de mistura completa para analisar a dinâmica do fósforo em 40 lagos e reservatórios localizados nas regiões Nordeste, Sudeste e Centro-Oeste do Brasil. Os resultados con- firmaram a dependência do coeficiente de decaimento de fósforo com o inverso da raiz quadrada do tempo de residência hidráulica. No entanto, em virtude da elevada temperatura da água dos lagos e reservatórios do Nordeste, esse coeficiente assumiu valores cerca de duas vezes superiores àqueles observados em regiões de clima tropical. Por outro lado, devido à alta variabilidade de temperatura dos lagos e reservatórios do Sudes- te, o coeficiente oscilou entre valores extremos observados em regiões de clima temperado e semiárido. Em virtude disso, propôs-se uma equação geral para calcular o coeficiente de decaimento de fósforo como uma função não apenas do tempo de residência hidráulica, mas também da temperatura da água. Após validação e análise de sensibilidade do modelo proposto, o mesmo foi aplicado a um reservatório hipotético sujeito a variações temporais de volume, vazão, carga e temperatura da água. Espera-se que este modelo simplificado possa auxiliar na gestão de lagos e reservatórios brasileiros. Palavras-chave: Eutrofização. Temperatura. Qualidade da água. Abstract Phosphorus is considered the main factor responsible for eutrophication of lakes and reservoirs. In the present study, a transient complete mixing model was used to analyse phosphorus dynamics in 40 lakes and reservoirs located in the Northeast, Southeast and Central-West regions of Brazil. The results confirmed the dependence of the phosphorus decay coefficient on the inverse of the square root of the hydraulic residence time. However, due to the high-water temperature of the lakes and reservoirs of the Northeast, this coefficient assumed values about two times higher than those observed in regions of tropical climate. On the other hand, due to the high temperature variability of the lakes and reservoirs in the Southeast, the coefficient oscillated between extreme values observed in temperate and semiarid regions. As a result, a general equation was proposed to calculate the phosphorus decay coefficient as a function not only of the hydraulic residence time, but also of the water temperature. After valida- tion and sensitivity analysis of the proposed model, it was applied to a hypothetical reservoir subject to temporal variations of water volume, flow, load and temperature. This simple model will potentially assist in the management of Brazilian lakes and reservoirs. Keywords: Eutrophication. Temperature. Water quality.