Numerical Modeling of Coastal Waves and Nearshore Currents on Adaptive Quadtree Grids

Coastal wave-induced nearshore currents are likely present as waves propagate and break on shallow-water zones. Accurate and efficient predictions of coastal waves and wave-induced nearshore currents in coastal areas are essential for coastal engineering. In this article, an efficient numerical model consisting of adaptive multilevel quadtree meshes for coastal waves and nearshore currents is presented. The numerical model consists of coastal wave and wave-induced nearshore-current models. In the model, coastal waves are modeled using the elliptic mild-slope equation that accounts for wave refraction, diffraction, reflection, and breaking-induced energy-dissipation effects, and nearshore currents are modeled using two-dimensional horizontal (2DH) depth-integrated shallow-water equations for which the wave radiation stresses for driving currents are provided by the wave model. The numerical model is solved using the finite-volume method on a Cartesian grid with an adaptive multilevel quadtree mesh system. The numerical mesh is adaptively refined according to local wavelengths, and the primary numerical grid is divided into four secondary grids if the local wavelength is smaller than eightfold the grid length. This allows the effective and accurate simulation of coastal waves and nearshore currents over complex topographies by a locally flexible refining grid resolution. The numerical model is validated by comparing the numerical results with experimental and field-measured results. The agreement between the numerical and measured data shows that the numerical model is both effective and efficient in modeling coastal waves and nearshore currents.