Boussinesq Equations in Geophysics

Xiaoping Xu
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Xiaoping Xu: Academy of Mathematics and System Science, Institute of Mathematics

Chapter Chapter 8 in Algebraic Approaches to Partial Differential Equations, 2013, pp 231-267 from Springer

Abstract: Abstract Boussinesq systems of nonlinear partial differential equations are fundamental equations in geophysical fluid dynamics. In this chapter, we use asymmetric ideas and moving frames to solve two-dimensional Boussinesq equations with partial viscosity terms and three-dimensional stratified rotating Boussinesq equations. We obtain new families of explicit exact solutions with multiple parameter functions; many of them are periodic, quasi-periodic, and aperiodic solutions that may have practical significance. Using Fourier expansion and some of our solutions, one can obtain discontinuous solutions. In addition, the symmetries of these equations are used to simplify our arguments.

Keywords: Rayleigh Number; Coriolis Force; Real Constant; Fourier Expansion; Nonlinear Partial Differential Equation (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-36874-5_8

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DOI: 10.1007/978-3-642-36874-5_8

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