Coastline Stress in Ocean Models
(IOM)

• Preamble
• Domain Rotation
• Results
• Analysis
• Conclusions
• Related Links

Preamble

Ocean models often allow a user to run the model with either "free-slip" or "no-slip" lateral boundary conditions imposed along the model coastline. The choice of particular coastline boundary condition impacts the model simulation, as has been shown by numerous studies. In particular, an undesirable behavior of the "free-slip" condition has been noted when the underlying numerical grid has a ragged coastline as compared to a straight coastline (Adcroft & Marshall, 1998). An understanding of the root cause of the undesirable behahvior, or a remedy for it, has yet to be offered. Here, we analyze the visocus terms in the ocean momentum equations and, via numerical simulation, demonstrate how true "free-slip" boundaries can be achieved -- independent of the raggedness of the model coastline.

Domain Rotation

The model full-domain extends from 5°W to 25°E and 25°N to 55°N. Within the full domain, the model ocean occupies a centered, sub-domain consisting of a 20° by 20 ° (possibly rotated) square domain. The particular domain, in which the model coordinates and the physical coordinates are co-aligned is demonstrated, where the color shading represents the variation of Coriolis parameter appropriate to a mid-latitude ocean basin (scaled by a factor of 10⁺⁴). The center coordinates of the model domain are 10°E longitude and 40°N latitude.

To explore the impact of coastline raggedness, experiments are designed in which the model-domain coordinates are held fixed while the physical-domain coordinates are rotated by some angle, theta. The parameter range of theta from 0 to 90 degrees, which corresponds to a counter clock wise rotation of the physical domain w.r.t. the model domain, is explored. The rotation of the physical domain is demonstrated in this animation (Windows .wmv format). The raggedness of the coastline is a function of the rotation angle theta -- maximum raggedness occuring at 45 degrees. The coastlines are rectilinear at theta of 0° and 90°, thus, the ocean simulation results will (should) be identical at these two special angles of rotation.

Both the model-domain and physical-domain coordinates are expressed in degrees of longitude and latitude. The domains are "locally-flat" such that a degree of longitude and latitude is everywhere equal to approximately 111 km, independent of rotation angle theta. The coordinate transformation from model longitude-latitude coordinates (X, Y) to physical longitude-latitude coordinates(X'', Y'') is a two-step process. First, a lateral shift from (X,Y) to (X',Y'), where the later represents the center coordinates of the model domain at 10°E longitude and 40°N latitude. Second, a rotation through an angle theta takes the coordinates (X',Y') into (X'', Y'') which are the physical-coordinates of the physical domain.

Numerical Experiments

Results

The results of the numerical experiments are summarized in the table below.

Analysis

... discuss KE as function of angle ... (how KE not change w.r.t. domain-rotation angle for "no-slip", but yes for "free-slip" but no for newly-introduced "no-stress" condition) ...

... theoretical digression goes here (stress w.r.t strain, navier-stokes vs. euler, mass conservation vs. momentum conservation, distinction (or not) between shear viscosity and bulk viscosity) ...

Conclusions

... traditional "free-slip" bcs are goodf/bad ? ...

... newly-introduced "no-stress" bcs are good/bad ? ...

Related Links

• What is the influence of indented walls on the oceanic circulation? (Dupont et al)

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