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An Effect of the Thermobaric Nonlinearity of the Equation of State: A Mechanism for Sustaining Solitary Rossby Waves

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  • 1 College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, Oregon
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Abstract

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 (θs) 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 θs 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)−1 or 0.7°C (1000 km)−1, from a θs 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.

Corresponding author address: Roland A. de Szoeke, College of Oceanic and Atmospheric Sciences, 104 Oceanography Administration Bldg., Oregon State University, Corvallis, OR 97331-5503. Email: szoeke@coas.oregonstate.edu

Abstract

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 (θs) 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 θs 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)−1 or 0.7°C (1000 km)−1, from a θs 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.

Corresponding author address: Roland A. de Szoeke, College of Oceanic and Atmospheric Sciences, 104 Oceanography Administration Bldg., Oregon State University, Corvallis, OR 97331-5503. Email: szoeke@coas.oregonstate.edu

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