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Interactions of flexural-gravity and interfacial waves in a two-layer fluid with a discontinuous background mean flow

Published online by Cambridge University Press:  16 July 2025

Susam Boral Open the ORCID record for Susam Boral [Opens in a new window] ,
Bao-Yu Ni Open the ORCID record for Bao-Yu Ni [Opens in a new window]  and
Alexander A. Korobkin
Susam Boral*
Affiliation:
College of Shipbuilding Engineering, Harbin Engineering University, Harbin, PR China Department of Civil, Structural and Environmental Engineering, Trinity College Dublin, Dublin, Ireland
Bao-Yu Ni
Affiliation:
College of Shipbuilding Engineering, Harbin Engineering University, Harbin, PR China
Alexander A. Korobkin
Affiliation:
School of Mathematics, University of East Anglia, Norwich, UK
*
Corresponding author: Susam Boral, susamboral@gmail.com
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Abstract

This study investigates the interactions between flexural-gravity waves and interfacial waves in a two-layer fluid, focusing on wave blocking. Both liquid layers are of finite depth bounded on top by a viscoelastic thin plate. Both liquids are incompressible and inviscid, and their flows are two-dimensional and potential. Linear wave theory and a linear equation of a thin floating viscoelastic plate of constant thickness are used. We analyse the phenomenon of wave blocking and Kelvin–Helmholtz (KH) instability in a two-layer fluid with a discontinuous background mean flow. A quartic dispersion relation for frequency as a function of wavenumber and other parameters of the problem is derived. Two cases of uniform current and layers moving with different velocities are studied. Wave blocking occurs when roots of the dispersion relation coalesce without accounting for plate viscosity, leading to zero group velocity. Our findings indicate that wave blocking can occur for both flexural-gravity and interfacial waves under various frequency and current speed conditions, provided that plate viscosity is absent. The role of different parameters and the flow velocities of the upper and lower layers are investigated in the occurrence of wave blocking and KH instability. The loci of the roots of the dispersion relation involving plate viscosity depict that no root coalescence occurs irrespective of the values of wavenumber and frequency in the presence of plate viscosity. The amplitude ratio of the interfacial wave elevation to that of floating viscoelastic plate deflection exhibits the dead-water phenomenon as a density ratio approaches unity.

JFM classification

Geophysical and Geological Flows: Ice sheets Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Stratified flows

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JFM Papers
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Journal of Fluid Mechanics , Volume 1015 , 25 July 2025 , A22
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© The Author(s), 2025. Published by Cambridge University Press

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Supplementary material: File

Boral et al. supplementary movie 1

Wave profiles of flexural-gravity waves in a two-layer fluid where the upper layer is moving over a stationary lower layer with $p_a = 0.1$ 1/m.
Download Boral et al. supplementary movie 1(File)
File 11.9 MB
Supplementary material: File

Boral et al. supplementary movie 2

Wave profiles of interfacial waves in a two-layer fluid where the upper layer is moving over a stationary lower layer with $p_a = 0.1$ 1/m.
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File 1.2 MB
Supplementary material: File

Boral et al. supplementary movie 3

Time domain simulation of the interfacial waves in a two-layer fluid with a floating viscoelastic plate-covered surface for $p_a = 0.2$ 1/m.
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File 4.9 MB
Supplementary material: File

Boral et al. supplementary movie 4

Loci of the roots of the flexural-gravity waves with retardation time for different values of frequency $\Omega$ in the vicinity of blocking point.
Download Boral et al. supplementary movie 4(File)
File 4.3 MB