 |
| Titel |
Physical vs. Numerical Dispersion in Nonhydrostatic Ocean Modeling |
| VerfasserIn |
Sean Vitousek, Oliver Fringer |
| Konferenz |
EGU General Assembly 2011
|
| Medientyp |
Artikel
|
| Sprache |
Englisch
|
| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 13 (2011) |
| Datensatznummer |
250045760
|
|
|
|
|
|
| Zusammenfassung |
| Many large-scale simulations of internal waves are computed with ocean models solving the
primitive (hydrostatic) equations. Internal waves, however, represent a dynamical balance
between nonlinearity and nonhydrostasy (dispersion), and thus may require computationally
expensive nonhydrostatic simulations to be well-resolved. Most discretizations of the
primitive equations are second-order accurate, inducing numerical dispersion generated from
odd-order terms in the truncation error (3rd-order derivatives and higher). This numerical
dispersion mimics physical dispersion due to nonhydrostasy. In this paper, we determine the
numerical dispersion coefficient associated with common discretizations of the primitive
equations. Comparing this coefficient with the physical dispersion coefficient from the
Boussinesq equations, we find that, to lowest order, the ratio of numerical to physical
dispersion is Π= Kλ2, where K is an O(1) constant dependent on the discretization of the
governing equations and λ is the grid leptic ratio, λ -¡ Δx-h1, where Δx is the horizontal
grid spacing and h1 is the depth of the internal interface. In addition to deriving
this relationship, we verify that it indeed holds in a nonhydrostatic ocean model
(SUNTANS). To ensure relative dominance of physical over numerical effects,
simulations require Î -ª 1. Based on this condition, the horizontal grid spacing
required for proper resolution of nonhydrostatic effects is λ < O(1) or Δx < h1.
When this condition is not satisfied, numerical dispersion overwhelms physical
dispersion, and modeled internal waves exist with a dynamical balance between
nonlinearity and numerical dispersion. Satisfaction of this condition may be a significant
additional resolution requirement beyond the current state-of-the-art in ocean modeling. |
|
|
|
|
|
|