Exact Formulas for Esimating the Area of Flow Regions in Free Boundary Problems

An effective technique is proposed for obtaining exact formulas for estimating the area of flow regions in two-dimensional fluid flow problems with free boundaries, that allow an exact solution in terms of elliptic functions. The effectiveness of the technique is demonstrated using a specific exampl...

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Bibliographic Details
Published in:Russian mathematics 2024-05, Vol.68 (5), p.66-71
Main Author: Alimov, M. M.
Format: Article
Language:English
Subjects:
Capillary flow
Capillary waves
Effectiveness
Elliptic functions
Exact solutions
Fluid flow
Free boundaries
Liquid surfaces
Mathematics
Mathematics and Statistics
Symmetry
Two dimensional flow
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Summary:An effective technique is proposed for obtaining exact formulas for estimating the area of flow regions in two-dimensional fluid flow problems with free boundaries, that allow an exact solution in terms of elliptic functions. The effectiveness of the technique is demonstrated using a specific example of the problem of capillary waves on the surface of a liquid of finite depth. This example is characterized by mirror symmetry of the flow region, but the technique can be generalized to the case of other symmetry of the flow region.
ISSN:1066-369X
1934-810X
DOI:10.3103/S1066369X24700361