The Impinging Jet Flow With Gravity In A Finitely Long Nozzle

The impinging jet flows with gravity are very common in engineering environments and nature,such as fountains and waterfalls.Based on a series of significant work on jet flows and cavity flows by H.Alt,L.Caffarelli,and A.Friedman,this thesis studies the impinging jet flow problem in the steady incompressible ideal fluid dynamics with gravity,establishes a mathematical theory of impinging jet flows with gravity in a finitely long nozzle,and proves that there is a smooth impinging jet flow for the mass flux,atmospheric pressure and initial velocity of the flow coming from the inlet of a finitely long nozzle,and a free boundary generated by the impinging jet flow is smoothly connected to the endpoint of the nozzle.Moreover,we investigate the regularity of the solution near the corner point on the nozzle inlet,the asymptotic behavior of the impinging jet flow at infinity,and the uniqueness of the parameters.The first chapter introduces the development of fluid mechanics,Euler equation,and the physical background of impinging jet flows and the impinging jet flows with gravity,and summarizes the previous studies both at home and abroad.Meanwhile,the mathematical definition of the impinging jet flow in a finitely long nozzle is given and the major findings of the thesis are presented in this chapter.In the second chapter,we will utilize the stream function and the variational method with parameters to prove the properties of the minimizer and the free boundary,and combines the regularity theory of the elliptic equation and the related theories of the free boundary to complete the proof of the main conclusions about the two-dimensional incompressible irrotational impinging jet flow.In the third chapter,we will list some further research related to jet problems with gravity.