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Atmospheric solitary waves: some applications to the morning glory of the Gulf of Carpentaria

Published online by Cambridge University Press:  26 April 2006

Lawrence K. Forbes  and
Shaun R. Belward
Lawrence K. Forbes
Affiliation:
Department of Mathematics, University of Queensland, St Lucia, Queensland 4072, Australia
Shaun R. Belward
Affiliation:
Department of Mathematics, James Cook University of North Queensland, Townsville 4811, Australia
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Abstract

A mathematical model is proposed to describe atmospheric solitary waves at the interface between a ‘shallow’ layer of fluid near the ground and a stationary upper layer of compressible air. The lower layer is in motion relative to the ground, perhaps as a result of a distant thunderstorm or a sea breeze, and possesses constant vorticity. The upper fluid is compressible and isothermal, so that its density and pressure both decrease exponentially with height. The profile and speed of the solitary wave are determined, for a wave of given amplitude, using a boundary-integral method. Results are discussed in relation to the ‘morning glory’, which is a remarkable meteorological phenomenon evident in the far north of Australia.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 321 , 25 August 1996 , pp. 137 - 155
Copyright
© 1996 Cambridge University Press

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References

Belward, S. R. & Forbes, L. K. 1995 Interfacial waves and hydraulic falls: some applications to atmospheric flows in the lee of mountains. J. Engng Maths 29, 161–179.Google Scholar
Benjamin, T. B. 1962 The solitary wave on a stream with an arbitrary distribution of vorticity. J. Fluid Mech. 12, 97–116.Google Scholar
Brown, D. J. & Christie, D. R. 1994 Fully nonlinear solitary waves in the lower atmosphere. Sixth Conf. on Mesoscale Processes, 18–22 July, Portland Oregon, pp. 194–196. American Meteorological Society, Boston. MA.
Christie, D. R. 1989 Long nonlinear waves in the lower atmosphere. J. Atmos. Sci. 46, 1462–1491.Google Scholar
Christie, D. R. 1992 The morning glory of the Gulf of Carpentaria: a paradigm for non-linear waves in the lower atmosphere. Austral. Met. Mag. 41, 21–60.Google Scholar
Christie, D. R. & Muirhead, K. J. 1983 Solitary waves: a hazard to aircraft operating at low altitudes. Austral. Met. Mag. 31, 97–109.Google Scholar
Clarke, R. H., Smith, R. K. & Reid, D. G. 1981 The morning glory of the Gulf of Carpentaria: an atmospheric undular bore. Mon. Weather Rev. 109, 1726–1750.Google Scholar
Davies-Jones, R. 1995 Tornadoes. Sci. Am. August, 34–41.Google Scholar
Drake, V. A. 1984 A solitary wave disturbance of the marine boundary layer over Spencer Gulf revealed by radar observations of migrating insects. Austral. Met. Mag. 32, 131–135.Google Scholar
Forbes, L. K. 1985 On the effects of non-linearity in free-surface flow about a submerged point vortex. J. Engng Maths 19, 139–155.Google Scholar
Forbes, L. K. & Belward, S. R. 1992 Atmospheric interfacial waves. Phys. Fluids A 4, 2222–2229.Google Scholar
Forbes, L. K. & Belward, S. R. 1994 Atmospheric interfacial waves in the presence of two moving fluid layers. Phys. Fluids 6, 3306–3316.Google Scholar
Haase, S. P. & Smith, R. K. 1984 Morning glory wave clouds in Oklahoma: a case study. Mon. Weather Rev. 112, 2078–2089.Google Scholar
Hunter, J. K. & Vanden-Broeck, J.-M. 1983 Accurate computations for steep solitary waves. J. Fluid Mech. 136 63–71.Google Scholar
Manasseh, R. & Middleton, J. H. 1995 Boundary-layer oscillations from thunderstorms at Sydney airport. Mon Weather Rev. 123, 1166–1177.Google Scholar
Miesen, R. H. M., Kamp, L. P. J. & Sluijter, F. W. 1990 Long solitary waves in compressible shallow fluids. Phys. Fluids A 2, 359–370.Google Scholar
Miles, J. W. 1980 Solitary waves. Ann. Rev. Fluid Mech. 12, 11–43.Google Scholar
Pullin, D. I. & Grimshaw, R. H. J. 1988 Finite-amplitude solitary waves at the interface between two homogeneous fluids. Phys. Fluids 31, 3550–3559.Google Scholar
Reeder, M. J., Christie, D. R., Smith, R. K. & Grimshaw, R. 1995 Interacting ‘morning glories’ over Northern Australia. Bull. Am. Met. Soc. 76, 1165–1171.Google Scholar
Rottman, J. W. & Einaudi, F. 1993 Solitary waves in the atmosphere. J. Atmos. Sci. 50, 2116–2136.Google Scholar
Schwartz, L. W. & Fenton, J. D. 1982 Strongly nonlinear waves. Ann. Rev. Fluid Mech. 14, 39–60.Google Scholar
Smith, R. K. 1988 Travelling waves and bores in the lower atmosphere: the ‘morning glory’ and related phenomena. Earth-Science Rev. 25, 267–290.Google Scholar
Smith, R. K. & Morton, B. R. 1984 An observational study of northeasterly ‘morning glory’ wind surges. Austral. Met. Mag. 32, 155–175.Google Scholar
Stoker, J. J. 1957 Water Waves. Wiley Interscience.
Teles DA Silva, A. F. & Peregrine, D. H. 1988 Steep, steady surface waves on water of finite depth with constant vorticity. J. Fluid Mech. 195, 281–302.Google Scholar
Turkington, B., Eydeland, A. & Wang, S. 1991 A computational method for solitary internal waves in a continuously stratified fluid. Stud. Appl. Maths 85, 93–127.Google Scholar
Vanden-Broeck, J.-M. 1994 Steep solitary waves in water of finite depth with constant vorticity. J. Fluid Mech. 274, 339–348.Google Scholar