Inertia-gravity waves trapped against a vertical barrier. (English) Zbl 0602.76019
Inertia-gravity waves trapped by a constant depth gradient against a vertical barrier are studied in an asymptotic limit (high frequency, weak depth gradient) of the shallow water equations; an f-plane is assumed. Both a numerical solution and an approximate analytical solution, which are in broad agreement, are presented. The waves display properties different from channel Kelvin and Poincaré waves and different from coastal waves. Implications of inertia-gravity wave trapping for geostrophic adjustment in a channel fluid model are explored.
MSC:
76B15 | Water waves, gravity waves; dispersion and scattering, nonlinear interaction |
35Q99 | Partial differential equations of mathematical physics and other areas of application |
86A05 | Hydrology, hydrography, oceanography |
76M99 | Basic methods in fluid mechanics |
Keywords:
barotropic wave propagation; Inertia-gravity waves; constant depth gradient; vertical barrier; asymptotic limit; shallow water equations; f- plane; numerical solution; approximate analytical solution; inertia- gravity wave trapping; geostrophic adjustment; channel fluid modelSoftware:
IMSL Numerical LibrariesReferences:
[1] | Abramowitz M., Handbook of Mathematical Functions (1972) · Zbl 0543.33001 |
[2] | Birkhoff G., Ordinary Differential Equations (1962) · Zbl 0102.29901 |
[3] | DOI: 10.1029/RG010i002p00485 · doi:10.1029/RG010i002p00485 |
[4] | DOI: 10.1175/1520-0469(1979)036<1205:MFEITA>2.0.CO;2 · doi:10.1175/1520-0469(1979)036<1205:MFEITA>2.0.CO;2 |
[5] | DOI: 10.1017/S0022112075001632 · Zbl 0315.76006 · doi:10.1017/S0022112075001632 |
[6] | Hyde R. A., Ph.D. Thesis, in: ”On the interaction between inertia-gravity normal modes and geostrophic currents in a simple fluid model,” (1982) |
[7] | DOI: 10.1175/1520-0469(1984)041<0038:TIOVRA>2.0.CO;2 · doi:10.1175/1520-0469(1984)041<0038:TIOVRA>2.0.CO;2 |
[8] | International Mathematical and Statistical Libraries. 1982. Texas: Houston. |
[9] | LeBlond P. H., Waves in the Ocean (1978) |
[10] | DOI: 10.1175/1520-0469(1968)025<1095:ATOTQB>2.0.CO;2 · doi:10.1175/1520-0469(1968)025<1095:ATOTQB>2.0.CO;2 |
[11] | DOI: 10.1017/S0022112072001685 · Zbl 0244.76006 · doi:10.1017/S0022112072001685 |
[12] | DOI: 10.1175/1520-0469(1964)021<0201:TSOCIT>2.0.CO;2 · doi:10.1175/1520-0469(1964)021<0201:TSOCIT>2.0.CO;2 |
[13] | Pedlosky J., Geophysical Fluid Dynamics (1979) · Zbl 0429.76001 · doi:10.1007/978-1-4684-0071-7 |
[14] | DOI: 10.1016/S0065-2156(08)70087-5 · Zbl 0471.76018 · doi:10.1016/S0065-2156(08)70087-5 |
[15] | DOI: 10.1111/j.2153-3490.1964.tb00189.x · doi:10.1111/j.2153-3490.1964.tb00189.x |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.