Background

In shelf regions with steep bathymetry in the presence of density gradients, the computation of the baroclinic pressure gradient term in 3D shallow water models may either become unstable or physically unrealistic. This manuscript examines four algorithms to compute the baroclinic pressure gradient term in finite element models. Two common systems for discretizing the vertical are sigma or z-level coordinates. In turn, permutations of these two coordinate systems serve as the basis for the four different algorithms examined herein. All are implemented in the context of the finite element hydrodynamic model, ADCIRC. Several density gradients that vary horizontally and vertically, with the pycnocline occurring at different depths, are used to evaluate the methods in a three-dimensional box grid with variable bathymetry. Initial testing, the subject of this work, focuses on model behavior for simplified problem with known analytic solutions. Long term goals for this study (the subject of subsequent papers) are three-fold: 1) to determine the vertical node placement algorithm that produces the most stable and physically realistic results; 2) to determine the interplay of vertical and horizontal resolution (and bathymetry and density profile), while considering simulation time; and 3) to produce accurate 3D flow fields and baroclinic pressure gradients. Outcomes from the study will be used to direct on-going modeling research in the Mississippi Sound