Kelvin waves on oceanic boundaries
- 12 September 1972
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Fluid Mechanics
- Vol. 55 (1) , 113-127
- https://doi.org/10.1017/s0022112072001685
Abstract
The primitive Kelvin wave (on a rotating, semi-infinite, plane sheet of water of uniform depth bounded by a vertical wall) is corrected for the effects of the Earth's curvature, the reduction in depth over the continental shelf, and bends in the coastline. The results are of interest for coastal propagation of the tides; numerical examples are given for the California coastline. It is found that the Earth's curvature reduces the wave speed south of Cape Mendocmo by 8–10% (the possible range for other coastlines is roughly ± 15%) and that the continental shelf reduces the wave speed by 2−8%. The off-shore mass transport (which vanishes identically for the primitive Kelvin wave) induced by curvature and/or the shelf also is calculated. The analysis of Packham & Williams (1968) for diffraction of a Kelvin wave by a corner is extended to obtain explicit results for the phase of the transmission coefficient. It is found that a sustained change in the direction of the coastline may induce a phase shift of the order of an hour (1·3 hours for the bend at Cape Mendocino), but that small distortions of the coastline without a sustained change in direction have negligible effects on the transmitted Kelvin wave at tidal frequencies.Keywords
This publication has 8 references indexed in Scilit:
- Kelvin wave attenuation along nearly straight boundariesJournal of Fluid Mechanics, 1972
- Nonlinear Kelvin and continental-shelf wavesJournal of Fluid Mechanics, 1972
- A note on tidal delay by inland seas and harborsGeophysical Fluid Dynamics, 1972
- The diffraction of tides by a narrow channelJournal of Fluid Mechanics, 1971
- Tides off‐shore: Transition from California coastal to deep‐sea waters‡Geophysical Fluid Dynamics, 1970
- Diffraction of Kelvin waves at a sharp bendJournal of Fluid Mechanics, 1968
- The fundamental solution for small steady three-dimensional disturbances to a two-dimensional parallel shear flowJournal of Fluid Mechanics, 1957
- The Genesis of the Double Gamma FunctionsProceedings of the London Mathematical Society, 1899