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These seminars (unless otherwise stated) will take place on Wednesdays at 4pm in Cruciform Building Room B1.03 on a bi-weekly basis - see the map for further details.
20 Feb 2019
Speaker: Alexander Doak (UCL)
Title: FREE-streamline flow
Abstract:
A broad set of problems in fluid dynamics come under the category ‘free-boundary problems’. They are characterised as problems where one or more boundaries of the flow domain are unknown, and must be found as part of the solution. These problems require two boundary conditions on the unknown boundary, usually given by a kinematic boundary condition, and continuity of pressure (dynamic boundary condition). When considering two-dimensional potential flow, there was interest in the 18th and early 19th century (Helmholtz, Kirchoff, Zhukovsky, Hoptkinson, Love, Rayleigh… to name a few) on what is known as free-streamline problems. These are problems where gravity and all other forces are ignored, such that the constant pressure condition on a free-surface is given by |velocity|=constant.
The interest stemmed partly from the fact that these fully nonlinear problems had known analytic solutions. These solutions were found using a variety of powerful theorems from complex analysis. In this talk, I will present a method assossiated to Love (1891), and later improved by Hoptkinson (1898), which, in the most generalised form, can be used to solve a two-dimensional potential flow, bounded solely by straight walls and free streamlines, even with singularities within the flow domain.