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Green’s functions for Rossby waves

Published online by Cambridge University Press:  02 October 2017

R. C. Kloosterziel*
School of Ocean and Earth Science and Technology, University of Hawaii, Honolulu, HI 96822, USA
L. R. M. Maas
Institute for Marine and Atmospheric Research, Utrecht University, Princetonplein 5, 3584CC Utrecht, The Netherlands Royal Netherlands Institute for Sea Research, P.O. Box 59, 1790AB Texel, The Netherlands
Email address for correspondence:


Compact solutions are presented for planetary, non-divergent, barotropic Rossby waves generated by (i) an impulsive point source and (ii) a sustained point source of curl of wind stress. Previously, only cumbersome integral expressions were known, rendering them practically useless. Our simple expressions allow for immediate numerical visualization/animation and further mathematical analysis.

© 2017 Cambridge University Press 

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Boyd, J. P. & Sanjaya, E. 2014 Geometrical effects of western intensification of wind-driven ocean currents: the stommel model, coastal orientation, and curvature. Dyn. Atmos. Oceans 65, 1738.CrossRefGoogle Scholar
Cahn, A. J. 1945 An investigation of the free oscillations of a simple current system. J. Meteorol. 2 (2), 113119.2.0.CO;2>CrossRefGoogle Scholar
Dickinson, R. E. 1969a Propagators of atmospheric motions 1. Excitation by point impulses. Rev. Geophys. 7 (3), 483514.CrossRefGoogle Scholar
Dickinson, R. E. 1969b Propagators of atmospheric motions 2. Excitation by switch-on sources. Rev. Geophys. 7 (3), 515538.CrossRefGoogle Scholar
Dixon, A. L. & Ferrar, W. L. 1933 Integrals for the products of two bessel functions. Q. J. Math. 4, 193208.CrossRefGoogle Scholar
Erdélyi, A.(Ed.) 1953 Higher Transcendental Functions, 3, vol. 2. McGraw-Hill.Google Scholar
Hough, S. S. 1898 On the application of harmonic analysis to the dynamical theory of the tides. Part ii. On the general integration of laplaces dynamical equations. Phil. Trans. R. Soc. Lond. A 191, 139185.CrossRefGoogle Scholar
Kamenkovich, V. M. 1989 Development of Rossby waves generated by localized effects. Oceanology 29 (1), 111.Google Scholar
Llewellyn-Smith, S. G. 1997 The motion of a non-isolated vortex on the beta-plane. J. Fluid Mech. 346, 149179.CrossRefGoogle Scholar
Longuet-Higgins, M. S. 1965 The response of a stratified ocean to stationary or moving wind-systems. Deep-Sea Res. 12, 923973.Google Scholar
Maas, L. R. M. 1989 A closed form green function describing diffusion in a strained flow field. SIAM J. Appl. Maths 49 (5), 13591373.CrossRefGoogle Scholar
Magnus, W., Oberhettinger, F. & Soni, R. P. 1966 Formulas and Theorems for the Special Functions of Mathematical Physics, 3rd edn. Springer.CrossRefGoogle Scholar
Margules, M. 1893 Luftbewegungen in einer rotierenden sphäroidschale (ii. teil). Sitz. der Math. - Naturwiss. Klasse, Kais. Akad. Wiss., Wien 102, 1156.Google Scholar
McKenzie, J. F. 2014 The group velocity and radiation pattern of Rossby waves. Geophys. Astrophys. Fluid Dyn. 108 (3), 258268.CrossRefGoogle Scholar
Moon, P. & Spencer, D. E. 1961 Field Theory Handbook. Springer.CrossRefGoogle Scholar
Morse, P. M. & Feshbach, H. 1953 Methods of Theoretical Physics. McGraw-Hill.Google Scholar
Olver, F. W. J., Lozier, D. W., Boisvert, R. F. & Clark, C. W.(Eds) 2010 NIST Handbook of Mathematical Functions. Cambridge University Press.Google Scholar
Pedlosky, J. 1987 Geophysical Fluid Dynamics, 2nd edn. Springer.CrossRefGoogle Scholar
Rhines, P. B. 1975 Waves and turbulence on a beta-plane. J. Fluid Mech. 69, 417443.CrossRefGoogle Scholar
Rhines, P. B. 2003 Rossby waves. In Encyclopedia of Atmospheric Sciences (ed. Holton, J. R., Curry, J. A. & Pyle, J. A.), pp. 137. Academic.Google Scholar
Rossby, C.-G. 1945 On the propagation of frequencies and energy in certain types of oceanic and atmospheric waves. J. Meteorol. 2 (4), 187204.2.0.CO;2>CrossRefGoogle Scholar
Rossby, C.-G. & Collaborators 1939 Relations between variations in the intensity of the zonal circulation of the atmosphere and the displacements of the semi-permanent centres of action. J. Mar. Res. 2, 3854.CrossRefGoogle Scholar
Veronis, G. 1958 On the transient response of a beta-plane ocean. J. Oceanogr. Soc. Japan 14 (1), 15.CrossRefGoogle Scholar
Webb, G. M., Duba, C. T. & Hu, Q. 2016 Rossby wave green’s functions in an azimuthal wind. Geophys. Astrophys. Fluid Dyn. 110 (3), 224258.CrossRefGoogle Scholar
Zimmerman, J. T. F. & Maas, L. R. M. 1989 Renormalized greens function for nonlinear circulation on the 𝛽 plane. Phys. Rev. A 39 (7), 35753590.CrossRefGoogle Scholar