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Flexural-gravity wave dynamics in two-layer fluid: blocking and dead water analogue

Published online by Cambridge University Press:  31 August 2018

S. Das Open the ORCID record for S. Das [Opens in a new window] ,
T. Sahoo  and
M. H. Meylan
S. Das*
Affiliation:
Department of Mathematics, Indian Institute of Information Technology Bhagalpur, Bhagalpur – 813210, India
T. Sahoo
Affiliation:
Department of Ocean Engineering and Naval Architecture, Indian Institute of Technology Kharagpur, Kharagpur 721302, India
M. H. Meylan
Affiliation:
School of Mathematical and Physical Sciences, University of Newcastle, NSW 2308, Australia
*
†Email address for correspondence: santudas20072@gmail.com
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Abstract

Flexural-gravity wave characteristics are analysed, in the presence of a compressive force and a two-layer fluid, under the assumption of linearized water wave theory and small amplitude structural response. The occurrence of blocking for flexural-gravity waves is demonstrated in both the surface and internal modes. Within the threshold of the blocking and the buckling limit, the dispersion relation possesses four positive roots (for fixed wavenumber). It is shown that, under certain conditions, the phase and group velocities coalesce. Moreover, a wavenumber range for certain critical values of compression and depth is provided within which the internal wave energy moves faster than that of the surface wave. It is also demonstrated that, for shallow water, the wave frequencies in the surface and internal modes will never coalesce. It is established that the phase speed in the surface and internal modes attains a minimum and maximum, respectively, when the interface is located approximately in the middle of the water depth. An analogue of the dead water phenomenon, the occurrence of a high amplitude internal wave with a low amplitude at the surface, is established, irrespective of water depth, when the densities of the two fluids are close to each other. When the interface becomes close to the seabed, the dead water effect ceases to exist. The theory developed in the frequency domain is extended to the time domain and examples of negative energy waves and blocking are presented.

JFM classification

Geophysical and Geological Flows: Ice sheets Geophysical and Geological Flows: Internal waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 854 , 10 November 2018 , pp. 121 - 145
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Copyright
© 2018 Cambridge University Press 

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Das et al. supplementary movie 1

Time--domain simulation of waves under the compressive force Q=√D. The top blue curve is the wave at the surface and the lower red curve is the wave at the interface.

Download Das et al. supplementary movie 1(Video)
Video 1.4 MB

Das et al. supplementary movie 2

Time--domain simulation of waves under the compressive force Q=1.95√D. The top blue curve is the wave at the surface and the lower red curve is the wave at the interface.

Download Das et al. supplementary movie 2(Video)
Video 871.3 KB