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On the streamline topology of inviscid flow with multiple points in a homogenous stream
Author(s) -
Kolonits F.
Publication year - 2008
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200700089
Subject(s) - streamlines, streaklines, and pathlines , inviscid flow , flow (mathematics) , simple (philosophy) , cylinder , point (geometry) , circulation (fluid dynamics) , geometry , mathematics , mathematical analysis , physics , topology (electrical circuits) , mechanics , combinatorics , philosophy , epistemology
Special streamlines in the flow with circulation around a cylinder cross themselves, maybe even three times. The simple crossing happens orthogonally, while the threefold one shows up π/3 angles among the branches. There are no discontinuous changes as the pattern develops with growing circulation. These observations yield a general statement. Here we show that if a z = F ( x , y ) is a solution of the Δ z = 0 Laplace equation and a z = const curve intersects itself (once or several times), then the branches running to that crossing point shall form equal angles.