Nonlinear Exact Solutions of the 2-Dimensional Rotational Euler Equations for the Incompressible Fluid-中国期刊网

摘要 Inthispaper,theClarkson–Kruskaldirectapproachisemployedtoinvestigatetheexactsolutionsofthe2-dimensionalrotationalEulerequationsfortheincompressiblefluid.Theapplicationofthemethodleadstoasystemofcompletelysolvableordinarydifferentialequations.Severalspecialcasesarediscussedandnovelnonlinearexactsolutionswithrespecttovariablesxandyareobtained.Itisofinteresttonoticethatthepressurepisobtainedbythesecondkindofcurvilinearintegralandthecoefficientsofthenonlinearsolutionsaresolitarywavetypefunctionsliketanh(kt/2)andsech(kt/2)duetotherotationalparameterk=0.SuchphenomenonneverappearintheclassicalEulerequationswhereintheCoriolisforcearisingfromthegravityandEarth’srotationisignored.Finally,illustrativenumericalfiguresareattachedtoshowthebehaviorsthattheexactsolutionsmayexhibit.

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Nonlinear Exact Solutions of the 2-Dimensional Rotational Euler Equations for the Incompressible Fluid

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Nonlinear Exact Solutions of the 2-Dimensional Rotational Euler Equations for the Incompressible Fluid

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