Nonlinear exact solutions of the 2-dimensional rotational Euler equations for the incompressible fluid

Hong-Li AN, Jin-Jing YANG, Man Wai YUEN

Research output: Contribution to journalArticle

Abstract

In this paper, the Clarkson-Kruskal direct approach is employed to investigate the exact solutions of the 2-dimensional rotational Euler equations for the incompressible fluid. The application of the method leads to a system of completely solvable ordinary differential equations. Several special cases are discussed and novel nonlinear exact solutions with respect to variables x and y are obtained. It is of interest to notice that the pressure p is obtained by the second kind of curvilinear integral and the coefficients of the nonlinear solutions are solitary wave type functions like tanh(kt/2) and sech (kt/2) due to the rotational parameter k ≠ 0. Such phenomenon never appear in the classical Euler equations wherein the Coriolis force arising from the gravity and Earth's rotation is ignored. Finally, illustrative numerical figures are attached to show the behaviors that the exact solutions may exhibit. Copyright © 2015 Chinese Physical Society and IOP Publishing Ltd.
Original languageEnglish
Pages (from-to)613-618
JournalCommunications in Theoretical Physics
Volume63
Issue number5
DOIs
Publication statusPublished - May 2015

Citation

An, H.-L., Yang, J.-J., & Yuen, M.-W. (2015). Nonlinear exact solutions of the 2-dimensional rotational Euler equations for the incompressible fluid. Communications in Theoretical Physics, 63(5), 613-618.

Keywords

  • Rotational Euler equations
  • Incompressible fluids
  • Clarkson–Kruskal direct method
  • Similarity re-ductions
  • Nonlinear exact solutions

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