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On Some Particular Cases of the Solution of Laplace's Equation Describing the Principal Properties of Vortex Formations in Fluids
Author(s) -
Dráský Jiří
Publication year - 1966
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.19660460202
Subject(s) - vortex , classical mechanics , gravitational singularity , discontinuity (linguistics) , physics , mechanics , mathematics , mathematical analysis
Vortex formations represent a particular case of discontinuous flow of fluids. For the most, they are non‐stationary formations with a pronounced whirling motion of intensity that is characterized by velocity circulation about the center, decreasing or increasing with time. They always contain a core with a marked component of rotational motion and one or two discontinuity surfaces or vortex layers rolling up in the form of spirals. In addition to the intensive whirling motion, they also exhibit centripetal or centrifugal motions. For cases where in the first approximation the effect of viscosity may be neglected and the medium considered an incompressible fluid, the paper demonstrates that all basic features of vortex formations may be described by a solution of Laplace's equation constructed as a convenient combination of algebraic and logarithmic singularities. The solution thus obtained is dependent on time insofar that all conditions of compatibility of the flow must be satisfied at all times in every point (particularly on the discontinuity surface). Several plane models of vortex formations are considered and with their aid a model is constructed of a flow field with vortex pair behind a cylinder starting from rest. A comparison of theoretical and experimental results is presented for this case.