40 horizontal x 30 vertical grid cells

The bore sharpens in the hydrostatic model and we se the development of a distinct vertical second mode. The second mode in the non-hydrostatic model is slightly more pronounced than for the coarse grid, but the coarse and medium grid non-hydrostatic results are roughly comparable

<download 2mb avi of hydrostatic>

<download 2mb avi of nonhydrostatic>

80 horizontal x 60 vertical grid cells

The hydrostatic bore is now extremely sharp and we see the development of two vertical second-mode waves. In contrast, the non-hydrostatic model shows behavior that is very similar to the coarser grids, with some extra compression in the vertical second mode.

Comments:

Unlike the non-hydrostatic model, the hydrostatic model does not appear to be converging to a particular solution as the grid is refined. Indeed, we are getting a better solution to the wrong set of equations, which has a feedback through accumulation of error and change in the modeled wave properties. As the model grid size decreases, this initially decreases the numerical dissipation and diffusion, which leads to greater steepening in the hydrostatic model. However, the greater steepening results in the development of wave patterns that effectively increase the numerical dissipation and diffusion. These concept will be demonstrated in a paper to be presented at the 17th ASCE Engineering Mechanics Conference, June 13-16, 2004 < http://chinacat.coastal.udel.edu/~kirby/EM2004 > in the session Fluid Mechanics of Lakes and Reservoirs II, at 1315 on June 13.