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...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.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No.11301269Jiangsu Provincial Natural Science Foundation of China under Grant No.BK20130665+2 种基金the Fundamental Research Funds KJ2013036 for the Central UniversitiesStudent Research Training under Grant No.1423A02 of Nanjing Agricultural Universitythe Research Grant RG21/2013-2014R from the Hong Kong Institute of Education
文摘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.
