Linear Surface Waves over Rotating Fluids
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 117, Issue 2
Abstract
Assuming that fluids are incompressible, inviscid, and homogeneous, natural linear surface waves in a rotating system can be decomposed into different frequency components. For each frequency component, solutions can be further decomposed into modes of an infinite series in the vertical direction. A depth‐integrated two‐dimensional model equation is derived to include Coriolis effects for waves of each mode propagating over variable depth topography in rotating fluids. The model equation reduces to the mild‐slope equation for waves in irro‐tational flows when Coriolis effects are ignored. It also reduces to an equation for waves in a rotating fluid of constant water depth. With respect to the Coriolis factor, propagating and evanescent modes of frequency components are distinguished. Analytical solutions for waves of the zeroth‐mode around a circular island on a paraboloidal water depth are obtained. Effects of the earth's rotation on wave response around a circular island are also discussed.
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References
1.
Berkhoff, J. C. W. (1972). “Computation of combined refraction‐diffraction.” Proc. of the 13th Int. Conf. Coastal Engineering, Vancouver, British Columbia, Canada, 471–490.
2.
Gill, A. E. (1982). Atmosphere‐ocean dynamics. Academic Press, San Diego, Calif.
3.
Homma, S. (1950). “On the behavior of seismic sea waves around circular island.” Geophys. Mag., 21, 199–208.
4.
Kawahara, M., Hasegawa, K., and Kawanago, Y. (1977). “Periodic tidal flow analysis by F. E. perturbation method.” Comp. Fl., 5, 175–189.
5.
Kirby, J. T. (1986). “A general wave equation for waves over rippled beds.” J. Fluid Mech., 162, 171–186.
6.
LeProvost, C., and Poncet, A. (1978). “F.E.M. for spectral modeling of tides.” Int. J. Numer. Meth. Engrg., 12, 853–871.
7.
Longuet‐Higgins, M. S. (1969). “On the trapping of long‐period waves round islands.” J. Fluid Mech., 37(4), 773–784.
8.
Lynch, D. R., and Werner, F. E. (1986). “Three‐dimensional harmonic model for linearized tidal circulation.” Proc. of the Sixth Int. Conf. on F.E. in Water Research, 505–514.
9.
Mysak, L. A. (1967). “On the theory of continental shelf waves.” J. Marine Res., 25, 205–227.
10.
Pearson, C. E., and Winter, D. F. (1977). “On the calculation of tidal currents in homogeneous estuaries.” J. Phys. Ocean, 7(4), 520–531.
11.
Smith, R., and Sprinks, T. (1975). “Scattering of surface waves by a conical island.” J. Fluid Mech., 72, 373–384.
12.
Tsay, T. K., and Liu, P. L.‐F. (1983). “A finite element model for wave refraction and diffraction.” Appl. Ocean Res., 5(1), 30–37.
13.
Snyder, R. L., Sidjabat, M., and Filloux, J. H. (1979). “A study of tides, setup and bottom friction in a shallow semi‐enclosed basin, Part II.” J. Phys. Ocean., 9, 170–188.
14.
Tsay, T. K., Zhu, W., and Liu, P. L.‐F. (1989). “A finite element model for wave refraction, diffraction, reflection and dissipation.” Appl. Ocean Res., 11(1), 33–38.
15.
Westerink, J. J., Connor, J. J., Stolzenbach, K. D. (1986). “Spectral computations within the bright of Abaco using a frequency‐time domain finite element model.” Proc. of the Sixth Int. Conf. on F.E. in Water Research, 569–578.
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Published In
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 117 • Issue 2 • March 1991
Pages: 156 - 171
Copyright
Copyright © 1991 ASCE.
History
Published online: Mar 1, 1991
Published in print: Mar 1991
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