Abstract
On the equatorial beta-plane, the response of the flow in the linear shallow water wave equations to wind stress which is a step function in time can be formally solved by Laplace transform integrals (multiplied by the usual Hermite functions). Although these transform integrals must evaluated numerically, it is still possible to analyze the oceanic response to jumps in the wind. The work of Anderson and Rowlands (J Mar Res 34(3):295–312, 1976) [1] and Cane and Sarachik (J Mar Res 35(2):395–432, 1977) [2] is the point of entry to the complex wave patterns that result.
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Notes
- 1.
Notational comment: Anderson and Rowlands use q and r to denote our sum and difference variables S and D, respectively. They work in terms of parabolic cylinder functions (asymptotically proportional to \(\exp (-0.25 y^{2})\) instead of Hermite functions, which are proportional to \(\exp (- 0.5 y^{2})\), so there are lots of unexpected factors of 2 in their paper.
References
Anderson DLT, Rowlands PB (1976) Role of inertia-gravity and planetary waves in response of a tropical ocean: to incidence of an equatorial Kelvin wave on a meridional boundary. J Mar Res 34(3):295–312
Cane MA, Sarachik ES (1977) Forced baroclinic ocean motions, II: the linear equatorial bounded case. J Mar Res 35(2):395–432
Anderson DLT, Rowlands PB (1976) Somali current response to southwest monsoon – importance of local and remote forcing. J Mar Res 34(3):395–417
Anderson DLT (1973) A low latitude spectral model using Chebyshev-parabolic cylinder functions. Report 7, GARP Programme on Numerical Experimentation W. G. N. E., World Meteorological Organization, Geneva
Cane MA, Sarachik ES (1976) Forced baroclinic ocean motions, I: the linear equatorial unbounded case. J Mar Res 34(4):629–665
Cane MA, Sarachik ES (1979) Forced baroclinic ocean motions, III: the linear equatorial basin case. J Mar Res 37(2):355–398
Cane MA, Sarachik ES (1981) The response of a linear baroclinic equatorial ocean to periodic forcing. J Mar Res 39:652–693
McCreary JP (1976) Eastern tropical ocean response to changing wind systems: with application to El Nino. J Phys Oc 6:623–645
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Boyd, J.P. (2018). Impulsive Forcing and Spin-Up. In: Dynamics of the Equatorial Ocean. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-55476-0_8
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DOI: https://doi.org/10.1007/978-3-662-55476-0_8
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