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Mode transformation of waves on the surface of a liquid covered by an elastic film of finite thickness

https://doi.org/10.59887/2073-6673.2025.18(1)-3

Abstract

The study of surface wave suppression due to oil product films and biogenic films in areas of catastrophic phytoplankton blooms is an important task in application to the problem of remote diagnostics of pollution on the sea surface. The peculiarity of such films in comparison with the well-studied case of quasi-monomolecular films of surfactants is a significant (on the order of or more than 1 micron) film thickness, the latter in this case is described as a layer of viscous liquid. This paper investigates wave damping on a water surface covered by a layer of another viscous fluid of finite thickness with an elastic boundary between them within the framework of linear theory. The features of two different types of wave modes, which for infinitely thin film are characterized as transverse (gravitational-capillary waves, GCW) and longitudinal (Marangoni waves, MW), are numerically analyzed. The evolution of these modes with increasing thickness of the top layer up to thicknesses much larger than the thickness of the viscous sublayer in the film is analyzed. It is shown that in some interval of interface elasticity, determined by the wavelength and viscosity of the top layer, a mutual transformation of the modes occurs at the thickness of the layer of the order of viscous sublayer thickness in the film. Namely, a wave that was GCW for an infinitely thin film, at film thicknesses greater than the thickness of the viscous sublayer, transitions to a MW, and vice versa. This effect arises because the GCW and MW are neither purely gravity-capillary nor purely dilatational. Laboratory experiments showed good agreement with the numerical results and confirmed the existence of the mode transformation effect.

About the Authors

I. A. Sergievskaya
A. V. Gaponov-Grekhov Institute of Applied Physics RAS ; Volga State University of Water Transport
Russian Federation

Scopus AuthorID: 6602742495, WoS ResearcherID: L-6146-2017 

46 Ulyanova Str., Nizhny Novgorod 903950 

5 Nesterova Str. Nizhny Novgorod 903950 



S. A. Ermakov
A. V. Gaponov-Grekhov Institute of Applied Physics RAS ; Volga State University of Water Transport
Russian Federation

Scopus AuthorID: 7006796194, WoS ResearcherID: L-6157-2017

46 Ulyanova Str., Nizhny Novgorod 903950 

5 Nesterova Str. Nizhny Novgorod 903950 



T. N. Lazareva
A. V. Gaponov-Grekhov Institute of Applied Physics RAS
Russian Federation

Scopus AuthorID: 54884797800, WoS ResearcherID: AAJ-4607-2021

46 Ulyanova Str., Nizhny Novgorod 903950 



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Review

For citations:


Sergievskaya I.A., Ermakov S.A., Lazareva T.N. Mode transformation of waves on the surface of a liquid covered by an elastic film of finite thickness. Fundamental and Applied Hydrophysics. 2025;18(1):31-40. https://doi.org/10.59887/2073-6673.2025.18(1)-3

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ISSN 2073-6673 (Print)
ISSN 2782-5221 (Online)