A note on the temporal and spatial attenuation of ocean waves

We study attenuation of free waves in the homogeneous ocean. Using the Cauchy–Riemann relations and then energy equation, we derive a novel equation that relates temporal and spatial decay to the energy dissipation in the fluid. In particular, for spatially damped waves we find that the attenuation...

Full description

Saved in:
Bibliographic Details
Published in:Ocean modelling (Oxford) 2022-07, Vol.175, p.102027, Article 102027
Main Author: Weber, Jan Erik H.
Format: Article
Language:English
Subjects:
Continental shelf waves
Group velocity
Surface gravity waves
Temporal and spatial damping
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We study attenuation of free waves in the homogeneous ocean. Using the Cauchy–Riemann relations and then energy equation, we derive a novel equation that relates temporal and spatial decay to the energy dissipation in the fluid. In particular, for spatially damped waves we find that the attenuation coefficient is inversely proportional to the group velocity. We discuss the consequences of this for continental shelf waves where the group velocity may tend to zero in wave number space, and hence the spatial attenuation coefficient may become infinitely large. We show that generally for a travelling wave solution, the spatial damping will remain unchanged in a frame of reference moving with the group velocity, revealing the different physics behind temporal wave damping and spatial wave damping. •Temporal and spatial wave damping is related to the energy dissipation.•The spatial damping rate is inversely proportional to the group velocity.•Energy may accumulate locally for continental shelf waves with zero group velocity.
ISSN:1463-5003
1463-5011
DOI:10.1016/j.ocemod.2022.102027