Kármán vortex street for the generalized surface quasi-geostrophic equation

We are concerned with the existence of periodic traveling-wave solutions for the generalized surface quasi-geostrophic equation (including incompressible Euler equation), also known as von Kármán vortex street. These solutions are of C 1 type, and are obtained by studying a semilinear problem on an...

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Bibliographic Details
Published in:Calculus of variations and partial differential equations 2023-07, Vol.62 (6), Article 168
Main Authors: Cao, Daomin, Qin, Guolin, Zhan, Weicheng, Zou, Changjun
Format: Article
Language:English
Subjects:
Analysis
Calculus of Variations and Optimal Control
Optimization
Control
Euler-Lagrange equation
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Regularization
Systems Theory
Theoretical
Traveling waves
Vortex streets
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Summary:We are concerned with the existence of periodic traveling-wave solutions for the generalized surface quasi-geostrophic equation (including incompressible Euler equation), also known as von Kármán vortex street. These solutions are of C 1 type, and are obtained by studying a semilinear problem on an infinite strip whose width equals to the period. By a variational characterization of solutions, we also show the relationship between vortex size, traveling speed and street structure. In particular, the vortices with positive and negative intensity have the same or different scaling size in our construction, which constitutes the regularization for Kármán point vortex street.
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-023-02518-2