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Simulating hydrostatic and non‐hydrostatic oceanic flows
Author(s) -
Iskandarani M.
Publication year - 2008
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1791
Subject(s) - hydrostatic equilibrium , primitive equations , mechanics , hydrostatic pressure , context (archaeology) , flow (mathematics) , boundary (topology) , boundary value problem , geology , classical mechanics , mathematics , geometry , physics , mathematical analysis , differential equation , paleontology , quantum mechanics , numerical partial differential equations
The thin aspect ratio of oceanic basins is simultaneously a complication to contend with when developing ocean models and an opportunity to simplify the equations of motion. Here we discuss these two aspects of this geometric feature in the context of hydrostatic and non‐hydrostatic ocean models. A simple analysis shows that the horizontal viscous operator in the hydrostatic primitive equations plays a central role in the specification of boundary conditions on the lateral vertical surfaces bounding the domain. The asymptotic analysis shows that for very thin aspect ratios the leading‐order flow cannot be closed unless additional terms in the equations are considered, namely either the horizontal viscous forces or the non‐hydrostatic pressure forces. In either case, narrow boundary layers must be resolved in order to close the circulation properly. The computational cost increases substantially when non‐hydrostatic effects are taken into account. Copyright © 2008 John Wiley & Sons, Ltd.