Parameter and resolution sensitivity of coastal models in buoyancy-driven flow simulations
Abstract
The sensitivity of coastal ocean models to resolution, grid ratio and diffusivity is tested using simulations of a buoyantly driven internal bore. Three classes of models are compared: hydrostatic (H), fully nonhydrostatic (NH), and quasi-hydrostatic (QH). In the classic H approximation the vertical momentum equation reduces to a balance between the vertical pressure gradient and the buoyancy of the water. In the NH model the pressure is determined from a 3D elliptic equation that is derived by taking the divergence of the N-S equations. For the QH approximation the vertical velocity and pressure are determined by an iteration procedure, involving only a 2D elliptic equation which is a great numerical advantage in 3D modeling. For horizontal to vertical grid ratios, r = dx/dz, < 3 both the QH and the NH models exhibit nonhydrostatic characteristics. The propagation speed of the bore is approximately the same in the NH and QH models and is close to the theoretical inviscid speed. In the NH models simulations the leading front of the bore, the rotor, and the mixing region behind the rotor are all well defined and agree with laboratory experiments and field measurements. Large amplitude internal waves are generated behind the mixing region and Kelvin-Helmholtz (K-H) instabilities grow on the internal waves. In contrast the QH model has almost no rotor behind the bore edge and no mixing region. Also QH models exhibits K-H instabilities on the plume-ambient fluid interface only for small diffusivities, A_h = A_z < 15 cm^2/s, vs. 50 cm^2/s or higher for the NH models. However, for large diffusivities A_h, A_z > 100 cm^2/s, both the rotor behind the bore front and the K-H instabilities disappear for all models. In general, for vertical to horizontal grid ratios r = dx/dz > 5, both the NH and QH models behave like H models. For the H models the propagation speed is strongly a function of numerical method and grid resolution. For centered differencing schemes the propagation speed of the front in the H models was much less than in the QH and NH models and decreased with increasing r. With an upwind differencing scheme the propagation speeds from the H models almost matches those from the QH and NH models. Furthermore, the vertical velocity in the H models increases dramatically with decreasing dx.
- Publication:
-
EGS - AGU - EUG Joint Assembly
- Pub Date:
- April 2003
- Bibcode:
- 2003EAEJA....12743P