Leandro Farina

Radiation of water waves by a heaving submerged horizontal disc

A thin rigid plate is submerged beneath the free surface of deep water. The plate performs small-amplitude oscillations. The problem of calculating the radiated waves can be reduced to solving a hypersingular boundary integral equation. In the special case of a horizontal circular plate, this equation can be reduced further to onedimensional Fredholm integral equations of the second kind. If the plate is heaving, the problem becomes axisymmetric, and the resulting integral equation has a very simple structure; it is a generalization of Love’s integral equation for the electrostatic field of a parallel-plate capacitor. Numerical solutions of the new integral equation are presented. It is found that the added-mass coefficientbecomes negative for a range of frequencies when the disc is sufficientlyclose to the free surface.

Scattering of water waves by a submerged disc using a hypersingular integral equation

The three-dimensional interaction between water waves and a submerged disc, in deep water, is considered. The problem is reduced to a hypersingular integral equation over the surface of the disc. The integral equation is solved numerically using an expansion-collocation method, generalizing a method used previously by Parsons and Martin for several two-dimensional water-wave problems. This method is shown to be very effective: it incorporates the known behaviour near the edge of the disc and it permits all hypersingular (finite-part) inegrals to be evaluated analytically. Numerical results are presented, with emphasis on the scattering properties of the submerged disc.

Hypersingular integral equations over a disc: convergence of a spectral method and connection with Tranter's method

Two-dimensional hypersingular equations over a disc are considered. A spectral method is developed, using Fourier series in the azimuthal direction and orthogonal polynomials in the radial direction. The method is proved to be convergent. Then, Tranter’s method is discussed. This method was devised in the 1950s to solve certain pairs of dual integral equations. It is shown that this method is also convergent because it leads to the same algebraic system as the spectral method.

Water wave radiation by a heaving submerged horizontal disk very near the free surface

The radiation of water waves by heaving horizontal disk at a shallow submergence depth is considered. The problem is formulated as a Fredholm integral equation. The resonant frequencies originating from the shallow submergence are examined and their locations are computed by a modified Newton’s method. The hydrodynamic coefficients in a neighborhood of a resonance pole are found to be represented by circles in the complex plane. An asymptotic approximation is obtained for small values of the submergence depth. The relationship between the small-submergence first order problem and the dock problem is explored and found to be clearly represented by the added mass and damping coefficients.

Dynamic and resuspension by waves and sedimentation pattern definition in low energy environments: guaíba lake (Brazil)

Pesquisas referentes a dinâmica sedimentar em lagos sao escassas e a maioria trata da distribuicao e textura dos sedimentos, sendo raras aquelas que fazem mencao ao padrao de ondas e suas relacoes com a ressuspensao destes sedimentos e suas consequencias. Este trabalho analisa as caracteristicas das ondas incidentes no Lago Guaiba (Brasil) por meio da utilizacao do SWAN (Simulating Waves Nearshore) e suas relacoes com a ressuspensao de sedimentos junto ao fundo. Os resultados mostraram que as maiores ondas incidentes atingiram 0.55 m, particularmente quando de ventos do quadrante S e SE e com velocidades maiores que 7 m/s. Em termos gerais, as caracteristicas das ondas seguem os padroes de intensidade e direcao dos ventos, atingindo seus maximos valores aproximadamente 1 ou 2 horas apos a velocidade de pico dos ventos. Em conclusao, os ambientes de sedimentacao do lago foram mapeados e classificados da seguinte forma: 1) Ambientes Depositionais (51% da area do lago); 2) Ambientes Transicionais (41%); e 3) Ambientes Erosionais ou de nao deposicao (8%).Como forma de contribuir a gestao ambiental da regiao, foram gerados subsidios referentes ao potencial de concentracao de material particulado em suspensao.

Approximation of ensemble members in ocean wave prediction

An efficient method for generating members in a ocean wave ensemble prediction system is proposed. A linearization of the wave model WAM is used to obtain approximations of the ensemble members. This procedure was originally introduced in a dynamical assimilation scheme where Green’s functions play a central role. The evaluation of member approximations can be carried out in a fraction of the time required by the full model integration. This aspect of the method suggests a way of increasing the ensemble size as well as refining the model resolution without increasing computational costs.

Ocean wave modes in the South Atlantic by a short-scale simulation

ABSTRACT The shortage of observational ocean wave data in the South Atlantic (SA) Ocean has resulted in numerical modelling becoming the most used tool for the investigation of wave climate in this oceanic region. In this article, the global model WAve Model (WAM) is used to simulate ocean waves in the SA from June 2006 to July 2007 with high time resolution. The four leading modes of the significant wave height, swell, wave peak period and surface wind velocity based on the empirical orthogonal functions (EOF) and singular value decomposition (SVD) methods are computed and analysed. The results show a number of specific characteristics present in the short-scale regime which emphasise and, in some cases, reduce some of the aspects of the global wave climate. The interaction between atmosphere and ocean has been found in several fields and modes that were examined. A relationship between tracks of extratropical cyclones are observed.

Resuspension and transport of fine sediments by waves over a thin layer of viscoelastic mud with erosion

Abstract A mathematical model for the one-dimensional mass transport describing the concentration evolution of suspended sediments over a viscoelastic mud layer in the presence of erosion is presented. Using a perturbation method, the problem is set in terms of the concentration of particles at the water–mud interface. Numerical results show considerable difference from the cases of rigid and non-erodible interfaces. A singular behaviour of the particles concentration is observed when the mud depth approaches a resonant value, associated with negative convection velocity.

Transporte e ressuspensao de sedimentos finos por ondas sobre um leito viscoelastico

Solucoes numericas da equacao do transporte unidimensional que descrevem a evolucao da concentracao de sedimentos suspensos sobre um leito viscoelastico foram obtidas para alguns casos particulares. Usando o modelo viscoelastico generalizado de [5] para definir a camada de lama viscoelastica, obtivemos uma nova equacao do transporte unidimensional para esse mesmo problema.

Interação de ondas da superfície do mar com obstáculos flutuantes e submersos

A interacao das ondas oceânicas com corpos flutuantes e submersos e um problema constantemente estudado e presente na literatura, como em [1]. Os principais casos estudados sao na presenca de uma superficie livre limitando o fluido. Em [3] e apresentado o caso conhecido como problema de doca, onde o obstaculo flutua. A solucao deste problema pode ser obtida resolvendo a equacao integral de contorno para um potencial de velocidade φ. O segundo caso, onde o corpo esta completamente submerso, e investigado em [2]. A principal caracteristica notada e a ocorrencia de frequencias ressonantes onde a forca hidrodinâmica assume maximos locais. Neste trabalho iremos estudar as ondas e suas implicacoes em estruturas rigidas com componentes finos submersos, que sao partes integrantes de plataformas construidas para atuarem na industria do petroleo. Inicialmente vamos considerar como obstaculo um disco plano. Matematicamente esse problema permite uma formulacao em termos de uma equacao integral cuja solucao pode ser obtida expandindo o potencial de velocidade em funcoes de Legendre. Supomos que os movimentos do fluido sao de pequena amplitude, simplesmente harmonicos e que o mesmo e incompressivel e nao viscoso. Denotamos por φ o potencial de velocidade e por [φ] a descontinuidade em φ sobre a superficie do disco. As condicoes satisfeitas por φ, sao a equacao de Laplace [...]