# Three-dimensional hydrodynamic model for wind-driven circulation

• C. L. N. Cunha
• A. C. Scudelari
• P. C. C. Rosman
Technical Paper

## Abstract

This paper presents the development of a three-dimensional hydrodynamic model for wind-driven circulation using the moving element method in the vertical discretization. As most three-dimensional models use sigma coordinate transformation in the vertical discretization, the use of the moving element method is an alternative to the latter, with the advantage that there is no need for fixed subdivision of the water column. In the proposed model, the coupling of two- and three-dimensional hydrodynamic model is considered. The shallow-water equations are integrated in the vertical direction, finite elements are employed in the spatial discretization, and finite differences in the time discretization, to resolve the position of the free surface (ζ), and the vertically integrated velocities components. The three-dimensional module is used to compute the velocity profiles. In the three-dimensional module is employed the moving element method in the vertical discretization. The efficiency of the model is demonstrated through the comparison of its results with laboratory experimental results and with another model that uses sigma coordinate transformation in the vertical discretization.

### Keywords

Three-dimensional model Semi-implicit model Shallow-water equation Wind-driven circulation

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© The Brazilian Society of Mechanical Sciences and Engineering 2018

## Authors and Affiliations

• C. L. N. Cunha
• 1
• A. C. Scudelari
• 2
• P. C. C. Rosman
• 3