Abstract
ABSTRACT In this paper, we consider a problem of a three-dimensional free surface flow over an obstacle lying on the bottom of an infinite channel. The flow is supercitical, irrotational, stationary and the fluid is ideal and incompressible. We linearize the problem, then by a Fourier expansion of the velocity potential, we reduce the three-dimensional problem to a sequence of two-dimensional problems for the Fourier coefficients. We take into account of the gravity and we neglect the effects of the superficial tension. These problems are formulated by the Laplace operator and the Neumann–Kelvin condition on the free surface of the fluid domain. Some a priori properties of the solution are given, they allow us to construct a space, where we can use Lax–Milgram's theorem, to prove the existence and the uniqueness of the solution of the two-dimensional problem. Then, this sequence of solutions of 2D-problems, gives us the unique solution of the considered three-dimensional problem.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
