Surface waves on vertically sheared flows : approximate dispersion relations

Kirby, James Thornton; Chen, Tsung-Muh

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Surface waves on vertically sheared flows : approximate dispersion relations

[PDF-3.40 MB]

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Personal Author:

Kirby, James Thornton ; Chen, Tsung-Muh

Kirby, James Thornton ; Chen, Tsung-Muh Less -
Corporate Authors:

University of Florida. Coastal and Oceanographic Engineering Department. ; Pacific Marine Environmental Laboratory (U.S.)

University of Florida. Coastal and Oceanographic Engineering Department. ; Pacific Marine Environmental Laboratory (U.S.) Less -
NOAA Program & Office:

OAR (Oceanic and Atmospheric Research) ; PMEL (Pacific Marine Environmental Laboratory)

OAR (Oceanic and Atmospheric Research) ; PMEL (Pacific Marine Environmental Laboratory) Less -
Description:

Assuming linear wave theory for waves riding on a weak current of 0(ε) compared to the wave phase speed, an approximate dispersion relation is developed to 0(ε²) for arbitrary current U(z) in water of finite depth. The 0(ε²) approximation is shown to be a significant improvement over the 0(ε) result, in comparison with numerical and analytic results. Various current profiles in the full range of water depths are considered. Comments on approximate action conservation and application to depth-averaged wave models are included.
Keywords:

[+]

Mathematical Models Water Waves
Series:

Technical report (University of Florida. Coastal and Oceanographic Engineering Program) UFL/COEL-TR/ ; 077
Document Type:

Technical Report
Funding:

Contract no. 40ABNR6711
Place as Subject:

United States
License:

https://creativecommons.org/publicdomain/zero/1.0/
Rights Information:

CC0 Public Domain
Compliance:

Library
Main Document Checksum:

[+]

urn:sha256:074b989233d7a10faa8f459e8623c839e7477ab5c2b7ddc24375e798cacc87db
Download URL:

https://repository.library.noaa.gov/view/noaa/47178/noaa_47178_DS1.pdf
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Surface waves on vertically sheared flows : approximate dispersion relations

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