Comparisons of non-hydrostatic and hydrostatic internal wave
propagation for a breaking wave
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Hydrostatic model
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Non-hydrostatic model
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20 horizontal x 15 vertical grid
cells
While the hydrostatic model cannot
reproduce the dynamics of an overturn (no surprise), the non-hydrostatic
model shows the wave breaking on the second period.
<download
3mb avi of hydrostatic>
<download
3mb avi of nonhydrostatic>
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40 horizontal x 30 vertical grid
cells
With the smaller grid resolution,
the hydrostatic model shows steeper waves, while the breaking behavior
in the non-hydrostatic model becomes more complex.
<download
3mb avi of hydrostatic>
<download
3mb avi of nonhydrostatic>
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80 horizontal x 60 vertical grid
cells
At the finest resolution, the
nonlinear steepening in the hydrostatic model leads to what appears
to be a breaking event - that is, the inertia of the fluid where
the steep front meets causes a density inversion. The dynamics of
the density inversion cannot be handled by the hydrostatic equation,
so the flow breaks up into grid scale mixing until it equilibrates.
However, the non-hydrostatic model can handle the density inversions
and shows the development of complex mixing behavior.
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Comments:
The above models are solved with the physical (molecular
and turbulent) viscosities and diffusivities set to zero. Thus,
as we refine the grid, any diffusion of mass or dissipation of energy
is exclusively numerical. In effect, as we refine the grid, our
numerical Reynolds number and our numerical Peclet number get larger.
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