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

• Published in: Journal of physical oceanography Vol. 34; no. 9; pp. 2042 - 2056
• Main Author: DE SZOEKE, Roland A
• Format: Journal Article
• Language: English
• Published: Boston, MA American Meteorological Society 01.09.2004
• Subjects: Density; Earth, ocean, space; Effects; Exact sciences and technology; External geophysics; Meteorology; Ocean temperature; Oceanography; Oceans; Seawater; Solitary waves; sea water; Rossby wave; Solitary wave; Baroclinic mode; salinity; oceanography; Nonlinearity; spatial variations; anomalies; equations of state; Baroclinic waves
• DOI: 10.1175/1520-0485(2004)034<2042:AEOTTN>2.0.CO;2
• ISSN: 0022-3670

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]