Determination of the Velocity Field of Doubly Periodic Potential Flows

We are interested in the problem of exact determination of the velocity field for potential flows initiated by an arbitrary doubly periodic system of hydrodynamic singularities. If we use the well-known formula for finding an elliptic function from its known singularities, then the field is determin...

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Bibliographic Details
Published in:Lobachevskii journal of mathematics 2022-10, Vol.43 (10), p.2918-2925
Main Author: Alimov, M. M.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Elliptic functions
Geometry
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Potential flow
Probability Theory and Stochastic Processes
Singularities
Velocity distribution
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Summary:We are interested in the problem of exact determination of the velocity field for potential flows initiated by an arbitrary doubly periodic system of hydrodynamic singularities. If we use the well-known formula for finding an elliptic function from its known singularities, then the field is determined up to an arbitrary additive constant. We formulate and solve auxiliary hydrodynamic problems to eliminate this ambiguity. Finally, using hydrodynamic terms, we give some proposition that allows us to uniquely determine the velocity field of any potential flow initiated by an arbitrary doubly periodic system of hydrodynamic singularities.
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080222130054