Topographic solitary waves and groups
DOI:
https://doi.org/10.1590/Keywords:
Topographic Rossby waves, Solitary waves, Topographic Rossby waves; Solitary waves;Abstract
We examine nonlinear topographic waves in barotropic, rigid lid models with a focus on how depth shapes can or cannot support solitary waves. Comparisons between the full equations and the quasigeostrophic system show that the conditions for vanishing nonlinearity are different and that the transition from cyclonic to anticyclonic solitary waves does not happen for the same topographic shape. For these dynamics, however, such waves only exist for a channel geometry when the long waves can become non-dispersive. We therefore examine wave groups since short waves can have an isolated cross-topographic structure. Group solitary waves are found and analyzed with a hyperbolic tangent topography representing the transition from the shelf to deep water.
References
ABLOWITZ, M. & SEGUR, H. 1981. Solitons and the inverse scattering transform, Society for Industrial and Applied Mathematics, Philadelphia, 425p.
ALLEN, J. 1975. Coastal trapped waves in a stratified ocean, J. Phys. Oceanogr. 5, 300-325.
BAKER-YEBOAH, S., FLIERL, G., SUTYRIN, G. & ZHANG, Y. 2010. Transformation of an Agulhas eddy near the continental slope, Ocean Science 6, 143-159.
CLARKE, R. 1971. Solitary and cnoidal planetary waves, Geophys. Fluid Dyn. 2, 343-354.
FLIERL, G. & HAINES, K. 1994. The decay of modons due to Rossby wave radiation, Phys. Fluids 6, 3487-3497.
FLIERL, G., LARICHEV, V., MCWILLIAMS, J. & REZNIK, G. 1980. The dynamics of baroclinic and barotropic solitary eddies, Dyn. of Atmos. and Oceans 5, 1-41.
GARRETT, C. 1979. Topographic Rossby waves off east Australia: identification and role in shelf circulation, J. Phys. Oceanogr. 9, 244-253.
HAMILTON, P. 2009. Topographic Rossby waves in the Gulf of Mexico, Prog. in Oceanogr. 82, 131.
JOHNS, W. & WATTS, D. 1986. Time scales and structure of topographic Rossby waves and meanders in the deep Gulf Stream, J. Mar. Res. 44, 267-290.
LARICHEV, V. & REZNIK, G. 1976. Twodimensional Rossby soliton: an exact solution, Rep. U.S.S.R. Acad. Sci. 231, 1077-1079.
LARSEN, L. 1965. Comments of "Solitary Waves in the Westerlies", J. Atmos. Sci. 22, 222-224.
LONG, R. 1964. Solitary waves in the westerlies, J. Atmos. Sci. 21, 197-200.
LOUIS, J., PETRIE, B. & SMITH, P. 1982. Observations of topographic Rossby waves on the continental margin off Nova Scotia, 12, 47-55.
MALANOTTE-RIZZOLI, P. 1980. Solitary Rossby waves over variable relief and their stability. Part II. Numerical experiments., Dyn. Atmos. Oceans 4, 261-294.
MALANOTTE-RIZZOLI, P. 1982. Planetary solitary waves in geophysical flows, Advances in Geophysics 24, 147-224.
MALANOTTE-RIZZOLI, P. & HENDERSHOTT, M. 1980. Solitary Rossby waves over variable relief and their stability. Part I. The analytical theory., Dyn. Atmos. Oceans 4, 247-260.
MOORE, D. & SAFFMAN, P. 1971. Structure of a line vortex in an imposed strain, in R. M Olsen J.H., Goldburg A. (ed.), Aircraft Wake Turbulence, Plenum, New York, 339-353.
OEY, L. & LEE, H. 2002. Deep eddy energy and topographic Rossby waves in the Gulf of Mexico, J. Phys. Oceanogr. 32, 3499-3527.
PICKART, R. 1995. Gulf Stream-generated topographic Rossby waves, J. Phys. Oceanogr. 25, 574-86.
SHU, Y., XUE, H., WANG, D., CHAI, F., XIE, Q., CAI, S., CHEN, R., CHEN, J., LI, J. & HE, Y. 2016. Persistent and energetic bottom-trapped topographic Rossby waves observed in the southern South China Sea, Scientific reports 6(1), 1-8.
STERN, M. E. 1975. Minimal properties of planetary eddies, J. Mar. Res. 40, 57-74.
THOMPSON, R. 1971. Topographic Rossby waves at a site north of the Gulf Stream, Deep Sea Res. and Oceanogr. Abstracts 18, 1-19.
THOMPSON, R. & LUYTEN, J. 1976. Evidence for bottom-trapped topographic Rossby waves from single moorings, Deep Sea Res. and Oceanogr. Abstracts 23, 629-635.
WANG, Q., ZENG, L., SHU, Y., LI, J., CHEN, J., HE, Y., YAO, J.AND WANG, D. & ZHOU, W. 2019. Energetic topographic Rossby waves in the northern South China sea, Jour. Phys. Oceanog. 49(10), 2697-2714.
WANG, X. 1992. Interaction of an Eddy with a Continental Slope, PhD Thesis, MIT-WHOI.
YAMAGATA, T. 1980. On the nonlinear modulation of planetary topographic waves in a rotating stratified ocean, Geophysical & Astrophysical Fluid Dynamics 16(1), 35-54.
ZHANG, Y., PEDLOSKY, J. & FLIERL, G. 2011. Shelf circulation and cross-shelf transport out of a bay driven by eddies from an openocean current. Part I: Interaction between a barotropic vortex and a steplike topography, J Phys. Oceanogr. 41, 889-910.
ZHAO, B. & TIMMERMANS, M. 2018. Topographic Rossby waves in the Arctic Ocean's Beaufort Gyre, Journal of Geophysical Research: Oceans 123(9), 6521-6530.
