Leandro Farina

• Ph.D. in Applied Mathemaics
• Professor (Full) at Federal University of Rio Grande do Sul

This paper presents the interactions between headland sand bypassing and overpassing at Santinho’s beach, Brazil. Santinho receives sediments from the south (Moçambique) through headland bypassing and supplies sediment to the north (Ingleses) via headland bypassing and overpassing processes. To understand these interactions we: 1) identified if bea...

Ocean eddy dipoles are among the most common mesoscale features and may be ubiquitous across the global oceans. However, wave–current interactions in their proximity have not been extensively studied. Here we examine the impact of surface currents on the wave field near an ocean eddy dipole. Using the WW3 wave model, we conducted idealized numerica...

Due to the chaotic behaviour of the differential equations which model the problem of predicting ocean waves variables, a well-known strategy to overcome the difficulties is to run several simulations, varying the initial condition, and averaging the result of each, creating an ensemble. In recent years, with the increase in available data and comp...

The impact of an elliptic disc submerged in water of infinite depth on radiation and scattering phenomena is analyzed employing linear water wave theory. The problem is tackled by reducing it into two-dimensional hypersingular integral equations over the surface of the disc. Utilizing a spectral method, where the hypersingularity is evaluated analy...

In this study, we developed and validated two wave ensemble prediction systems (WEPS) to forecast wave conditions along the southeastern coast of Australia. Using the SWAN model (GEN3 ST6), we integrated complex bathymetric features with an unstructured grid and validated model outputs against buoy observations from Sydney, Port Kembla, and Bateman...

Offshore wind energy is vital for achieving global renewable energy goals, with Brazil holding significant untapped potential. This study focuses on the northeast coast of Brazil, particularly Rio Grande do Norte, where future wind farms are planned. By comparing coupled atmosphere-wave models (WRF+SWAN) with stand-alone atmospheric models, we anal...

This paper investigates the sensitivity of offshore wind simulations, focusing on the northeast coast of Brazil. The study utilizes the Coupled Ocean-Atmosphere-Wave-Sediment Transport Modeling System (COAWST), integrating the Weather Research and Forecasting (WRF) and Simulating Waves Nearshore (SWAN) models. The research emphasizes the impact of...

The airfoil integral equation over two disjoint intervals, separated by a distance κ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\kappa $$\end{document}, is consider...

In the present paper, the radiation and scattering by an elliptic disc submerged in infinite-depth water are investigated. The problems are solved by reducing them to two-dimensional hyper-singular integral equations over the surface of the disc. A spectral method is used to solve the integral equation numerically. Numerical results are presented f...

The forecast of wave variables are important for several applications that depend on a better description of the ocean state. Due to the chaotic behaviour of the differential equations which model this problem, a well know strategy to overcome the difficulties is basically to run several simulations, by for instance, varying the initial condition,...

We present a new deep learning training framework for forecasting significant wave height on the Southwestern Atlantic Ocean. We use the long short-term memory algorithm (LSTM), trained with the ERA5 dataset and also with buoy data. The forecasts are made for seven different locations in the Brazilian coast, where buoy data are available. We consid...

This paper is concerned mainly with the deceptively simple integral equation \[ u(x) - \frac{1}{\pi}\int_{-1}^{1} \frac{\alpha\, u(y)}{\alpha^2+(x-y)^2} \, \rd y = 1, \quad -1\ \leq x \leq 1, \] where $\alpha$ is a real non-zero parameter and $u$ is the unknown function. This equation is classified as a Fredholm integral equation of the second kind...

The use of satellite data to calibrate ocean wave spectrum partitions are being carried out in recent wave hindcast datasets as a way of correcting historical sea state records. The directional correction method aims at establishing separate fitting coefficients, for windsea and swell partition, as well as for the different sectors from which the w...

We present a framework for forecasting significant wave height on the Southwestern Atlantic Ocean using the long short-term memory algorithm (LSTM), trained with the ERA5 database available through Copernicus Climate Data Store (CDS) implemented by ECMWF (European Center for Medium Range Forecast) and also with buoy data. The predictions are made f...

This work investigates the sensitivity of the SWAN model with respect to state-of-the-art wave and wind datasets. The wave model was implemented and validated for the Southern Brazilian nearshore environment and simulated for 2015. Nine combinations of wave and wind datasets have been considered, aiming at establishing the boundary conditions and a...

Modes of variability in ocean wave conditions are coupled to atmospheric circulation changes due to exchange of energy and momentum at the interface. Here, we explored for the South Atlantic Ocean the relations between three main climate oscillations (El Niño–Southern Oscillation [ENSO], Southern Annular Mode [SAM], and Pacific Decadal Oscillation...

An algorithm for representing irregular satellite data obtained from advanced synthetic aperture radar (ASAR) uniformly in space and time is introduced and comparison with WAVEWATCH III model (WW3) data is carried out. Swell global data for 2007 are analysed using statistical parameters such as bias and scattering index. Satellite data showed a gre...

General propagation patterns due to the multiple interaction of waves and seamounts located in Northeast Brazil are investigated using SWAN. After conducting a model sensitivity test using in situ data, four realistic cases (in which the maximum period of the incoming swells was 17.6s) and one synthetic case (using the maximum period as 21.3s) have...

A thin circular porous plate is submerged below the free surface of deep water. The problem is reduced to a hypersingular integral equation of the second kind over the surface of the unit disc. The solution is computed by a spectral method known to be efficient for the case of a solid plate. Numerical results are presented for the heave added mass...

This paper is concerned mainly with the deceptively simple integral equation \[ u(x) - \frac{1}{\pi}\int_{-1}^{1} \frac{\alpha\, u(y)}{\alpha^2+(x-y)^2} \, \rd y = 1, \quad -1 \leq x \leq 1, \] where $\alpha$ is a real non-zero parameter and $u$ is the unknown function. This equation is classified as a Fredholm integral equation of the second kind...

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 di...

A thin nearly circular plate is submerged below the free surface of deep water. The problem is reduced to a hypersingular integral equation over the surface of the plate which is conformally mapped onto the unit disc. The solution is computed by a spectral method proved to be efficient for the case of a circular disc. Numerical results are presente...

The airfoil equation is considered over two disjoint intervals. Assuming the distance between the intervals is small an approximate solution is found and relationships between this approximation and the solution of the classical airfoil equation are obtained. Numerical results show the convergence of the solution of the original problem to the appr...

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...

Um método de aproximação de Fourier é utilizado para a modelagem e simulação de ondas completamente não lineares permanentes. O conjunto de equações não lineares resultante é resolvido pelo método de Newton. O empinamento de ondas é simulado, usando como base, comparações com dados experimentais. As alturas e ângulos de quebra são analisados até o...

Using the wave model SWAN (simulating waves nearshore), high waves on the southwestern Atlantic generated by extra-tropical cyclones are simulated from 2000 to 2010, and their impact on the Rio Grande do Sul (RS) coast is studied. The modeled waves are compared with buoy data and good agreement is found. The six extreme events in the period that pr...

We present a high resolution analysis of the interaction of irregular waves with natural and urban structures leading to extreme wave runup. Horizontal runup data, instantaneous flooding maps, and wave propagation beyond the coastline are numerically predicted. The novel methodology combining the Wave Watch III, SWAN and SWASH models to achieve acc...

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 integr...

Using the model SWAN, high waves on the Southwestern Atlantic generated by extra-tropical cyclones are simulated from 2000 to 2010 and their impact on the Rio Grande do Sul coast is studied. The modeled waves are compared with buoy data and good agreement is found. The six extreme events in the period which presented significant wave heights above...

Little research has been undertaken into sediment dynamics in lakes, and most of it only analyses particular aspects such as the texture of the sediments. In this study, the characteristics of the wave field in Guaíba Lake are investigated. The parameters significant wave height (Hs), period (T) and direction of wave propagation are examined togeth...

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 resolutio...

A thin circular body is submerged below the free surface of deep water. The problem is reduced to a hypersingular integral equation over the boundary of the body. Using a perturbation method, the problem is then reformulated by a sequence of simpler hypersingular equations over a flat disc making it well suited for an efficient previously used solu...

The availability of observational ocean wave data in the South Atlantic Ocean (SAO) is still very limited. Due to this shortage of data obtained in situ, numerical modeling has become the most used tool for the investigation of wave climate in whole world. Here, the global model WAM was used to simulate waves from June 2006 to July 2007 in order to...

This research examines the characteristics of Lake Guaíba’s waves with regard to their main parameters; significant wave height (Hs), period (T), direction of wave propagation and its connections with the ressuspension of sediments at the bottom. To this end, SWAN (Simulating Waves Nearshore) a type of software using mathematical modeling technique...

Contains reports on five research projects.

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 neighborhoo...

Pesquisas referentes à dinâmica sedimentar do Lago Guaíba são escassas e a maioria trata da distribuição e textura dos sedimentos, sendo raras aquelas que fazem menção ao padrão de ondas e suas relações com a ressuspensão destes sedimentos e suas consequências. A presente pesquisa analisa, por meio da aplicação do software SWAN (Simulating Waves Ne...

Researches on the sediment dynamics of Lake Guaiba are scarce, and most of them analyses just some aspects like texture of the sediments. This research examines the characteristics of Guaíba's Lake waves with regard to their main parameters; significant wave height (Hs), period (T), direction of wave propagation and its connections with the resuspe...

Synthesis of Hydrodynamics and Sedimentology ocean beaches of Rio Grande do Sul. In Portugues.

The ensemble numerical prediction of ocean waves is considered and all published works on this new topic in Geosciences are reviewed. A Wave Ensemble Prediction System is described where a global third-generation wave model is adopted. Twenty members are generated by a method based on Empirical Orthogonal Functions and a particular realistic case w...

The ensemble numerical prediction of ocean waves is considered and all published works on this new topic in Geosciences are reviewed. A Wave Ensemble Prediction System is described where a global third-generation wave model is adopted. Twenty members are generated by a method based on Empirical Orthogonal Functions and a particular realistic case w...

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 approxima...

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 approxima...

The problem of optimization of analytical and numerical approximations of Hasselmann's nonlinear kinetic integral is discussed in general form. Considering the general expression for the kinetic integral, a principle to obtain the optimal approximation is formulated. From this consideration it follows that the most well-accepted pproximations, such...

The numerical ensemble prediction is a well accepted method for improving the performanceof atmospheric models. In the context of ocean wave modeling little has been researched ordocumented about this technique. An essential study of the method of ensemble predictionapplied to deep water waves has been carried out. A framework is defined for obtain...

The numerical ensemble prediction is a well accepted method for improving the performance of atmospheric models. In the context of ocean wave modeling little has been researched or documented about this technique. An essential study of the method of ensemble prediction applied to deep water waves has been carried Out. A framework is defined for obt...

The evaluation of nearly singular single layer potentials encountered in boundary element methods is treated by a new approach. The potential is expressed as a sum of a one-dimensional integral and a correction term that vanishes for planar surfaces. The small variance of the second term's integrand allows the use of a quasi-Monte Carlo quadrature....

A novel application of the boundary integral method to horizontal well analysis in the field of petroleum engineering is presented. The transient pressure satisfies the heat equation, non-local and non-linear boundary conditions. The turbulent Row inside the well is modelled by considering a pressure gradient along the well. The heat potential is u...

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...

We present a precise derivation of the equations of motion of singular point vortices based on a weak formulation of Euler's equation for the flow of an incompressible fluid flow. Next we investigate a fast numerical method for the integration of these equations based on the Fast Multipole Method. We apply it to the motion of vortex patches and det...

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 one-dimensi...

We show that various problems involving the interaction of water waves with thin plates can be reduced to hypersingular boundary integral equations. Examples include scattering by submerged curved plates and by surface-piercing plates in two dimensions; trapping of waves by submerged plates; and scattering by submerged flat plates in three dimensio...

. We present a precise derivation of the equations of motion of singular point vortices based on a weak formulation of Euler's equation for the flow of an incompressible fluid flow. Next we investigate a fast numerical method for the integration of these equations based on the Fast Multipole Method. We apply it to the motion of vortex patches and d...