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Dynamic Convection in a Sea

In: Algebraic Approaches to Partial Differential Equations

Author

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  • Xiaoping Xu

    (Academy of Mathematics and System Science, Institute of Mathematics)

Abstract

The rotation of the earth influences both atmospheric and oceanic flows. In fact, the fast rotation and small aspect ratio are two main characteristics of large-scale atmospheric and oceanic flows. The small aspect ratio characteristic leads to primitive equations, and the fast rotation leads to quasi-geostrophic equations. A main objective in climate dynamics and in geophysical fluid dynamics is to understand and predict the periodic, quasi-periodic, aperiodic, and fully turbulent characteristics of large-scale atmospheric and oceanic flows. The general model of atmospheric and oceanic flows is very complicated. In this chapter, we study a simplified model of dynamic convection in a sea due to Ovsiannikov. First we perform a symmetry analysis on the equations. Then we use a new moving-line variable to solve the equations. An approach that uses the product of the cylindrical invariant function with the vertical variable is introduced. Finally, we reduce the three-dimensional (spatial) equations into a two-dimensional problem and then solve it using three different ansatzes (assumptions).

Suggested Citation

  • Xiaoping Xu, 2013. "Dynamic Convection in a Sea," Springer Books, in: Algebraic Approaches to Partial Differential Equations, edition 127, chapter 0, pages 213-230, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-36874-5_7
    DOI: 10.1007/978-3-642-36874-5_7
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