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Regular and singular components of 2D periodic fluid flows on a surface of viscous stratified fluid
Author NameAffiliationPostcode
Chashechkin Yuli Dmitrievich Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow 119526, Russia 119526
Ochirov Artem Alexandrovich* Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow 119526, Russia 119526
Lapshina Kristina Yurevna Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow 119526, Russia 119526
Trifonova Ulyana Olegovna Yaroslavl State University, Yaroslavl 150003, Russia 150003
Abstract:
The modern definition of the wave concept, which is based on the functional connection between the parameters of the spatial structure of an instantaneous flow pattern and the characteristics of the temporal variability at a given point, is discussed. The dispersion relation for 2D plane periodic perturbations on a surface of viscous stratified fluid is selected as a characteristic function defining the wave motion. Using the theory of singular perturbations, a method for calculating complete solutions to the dispersion relations of periodic flows, including regular wave and singular ligament solutions is presented. Properties of complete exact solution of the dispersion relation containing regular and singular functions are compared with asymptotic solutions. In limiting cases, obtained dispersion relations are matched with well-known expressions for waves in homogeneous viscous and ideal liquids.
Key words:  Navier-Stokes equation, periodic flows, theory of singular perturbations, asymptotic methods, surface capillary-gravity waves, ligaments, flow structure
DOI：10.11916/j.issn.1005-9113.2025014
Clc Number:O4
Fund:

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