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| Titel |
Approximation schemes to dispersion and linear problems for 3D systems on shear current of arbitrary direction and depth dependence |
| VerfasserIn |
Simen Ådnøy Ellingsen, Yan Li, Benjamin K. Smeltzer |
| Konferenz |
EGU General Assembly 2017
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| Medientyp |
Artikel
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| Sprache |
en
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 19 (2017) |
| Datensatznummer |
250143059
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| Publikation (Nr.) |
 EGU/EGU2017-6748.pdf |
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| Zusammenfassung |
| We compare different methods of approximating the dispersion relation for waves on top of
currents whose direction and magnitude may vary arbitrarily with depth. Two fundamentally
different approximation philosophies are in use: analytical approximation schemes, and what
we term the N-layer procedure in which the velocity profile is approximated by a
continuous, piecewise linear function of depth. The relative virtues of both schemes are
reviewed.
The N-layer procedure yields the dispersion relation with arbitrary accuracy. We present
the details and subtleties of implementing this procedure in practice. We find with a good
choice of layer boundaries, 4-5 layers are sufficient for accuracy of about 1%. For
inhomogeneous systems with a specified source, implementation is straightforward and most
complications are eschewed.
Analytical approximation schemes are reviewed, and criteria of applicability are
derived for the first time. In particular the much used approximation by Kirby &
Chen (1989) (KCA) is compared with a new approximation which we propose.
The two give similar predictions when the KCA is applicable, but our new scheme
is more robust and can handle several special but realistic cases where the KCA
fails.
Once the dispersion relation is calculated, 3D linear problems such as initial value
problems, or problems with stationary or periodic time dependence can be readily solved. |
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