摘要
In this paper, the Clarkson-Kruskal direct approach is employed to investigate the exact solutions of the 2-dimensionai rotationai 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 ≠ O. 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.
基金
Supported by the National Natural Science Foundation of China under Grant No.11301269
Jiangsu Provincial Natural Science Foundation of China under Grant No.BK20130665
the Fundamental Research Funds KJ2013036 for the Central Universities
Student Research Training under Grant No.1423A02 of Nanjing Agricultural University
the Research Grant RG21/2013-2014R from the Hong Kong Institute of Education
