An effect of the thermobaric nonlinearity of the equation of state: A mechanism for sustaining solitary Rossby waves

The thermobaric nonlinearity in the equation of state for seawater density-namely, the dependence of thermal expansibility on pressure-coupled with spatial variation of the oceanic temperature-salinity (θ-s) relation generates a nonlinear behavior in the buoyant force that can counter the linear dis...

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Bibliographic Details
Published inJournal of physical oceanography Vol. 34; no. 9; pp. 2042 - 2056
Main Author DE SZOEKE, Roland A
Format Journal Article
LanguageEnglish
Published Boston, MA American Meteorological Society 01.09.2004
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Summary:The thermobaric nonlinearity in the equation of state for seawater density-namely, the dependence of thermal expansibility on pressure-coupled with spatial variation of the oceanic temperature-salinity (θ-s) relation generates a nonlinear behavior in the buoyant force that can counter the linear dispersion of baroclinic Rossby waves and produce solitary waves. A Korteweg-deVries equation is derived in which the coefficient of the nonlinear term depends on the thermobaric parameter and the spatial gradient of the anomaly of the θ-s relation. Quantitative estimates can be made of the magnitude of the effect in terms of these parameters. For example, given first-baroclinic-mode spatial variations of order 0.1 psu (1000 km)^sup -1^ or 0.7°C (1000 km)^sup -1^, from a θ-s relation with a density ratio of 2, a solitary Rossby wave of maximum vertical displacement of approximately 100 m and horizontal scale of approximately 30 baroclinic Rossby radii of deformation can be generated. [PUBLICATION ABSTRACT]
ISSN:0022-3670
1520-0485
DOI:10.1175/1520-0485(2004)034<2042:AEOTTN>2.0.CO;2