Review of Recent Developments in Tidal Hydrodynamic Modeling. I: Spectral Models

Abstract

In this paper we present a brief overview, with a comprehensive set of references to recently published papers for detail, of a range of techniques used in tidal hydrodynamic modeling and recent progress in the field. Although the paper aims to introduce the topic to someone new to the area, the main emphasis is on new developments in near coastal (shallow sea) tidal modeling, and consequently we concentrate on three-dimensional modeling, which has progressed significantly in recent years. The paper gives a brief account of methods used to discretize the hydrodynamic equations in the horizontal, namely finite difference, finite element and boundary-fitted coordinates, and through time. The representation of tidal current structure in a three-dimensional model using a spectral method in the vertical is also described. In this method the subgrid scale vertical diffusion of momentum, which has a major influence on tidal current profiles, is parameterized using a flow-dependent eddy viscosity. Recent work on the chaotic behavior of particles released into two-dimensional tidal flow models and the use of adjoint models is also briefly considered.