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Citation:
　Piyali Kundu,Rumpa Chakraborty.Gravity Wave Generated by Initial Axisymmetric Disturbance at the Surface of an Ice-covered Ocean with Porous Bed[J].Journal of Marine Science and Application,2021,(4):632-645.[doi:10.1007/s11804-021-00241-y]
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Gravity Wave Generated by Initial Axisymmetric Disturbance at the Surface of an Ice-covered Ocean with Porous Bed

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Title:
Gravity Wave Generated by Initial Axisymmetric Disturbance at the Surface of an Ice-covered Ocean with Porous Bed
Author(s):
Piyali Kundu1;  Rumpa Chakraborty2
Affilations:
Author(s):
Piyali Kundu1;  Rumpa Chakraborty2
1. Department of Science & Humanities, North Calcutta Polytechnic, Cossipore, Kolkata, 700002, India;
2. Department of Mathematics, Diamond Harbour Women’s University, South 24 Parganas, Pin-743368, Sarisha, India
Keywords:
Axisymmetric disturbances and ice-covered ocean|Porous bottom|Laplace and Hankel transform|Method of stationary phase|Free surface depression|Phase velocity and group velocity
分类号:
-
DOI:
10.1007/s11804-021-00241-y
Abstract:
This paper is concerned with the generation of gravity waves due to prescribed initial axisymmetric disturbances created at the surface of an ice sheet covering the ocean with a porous bottom. The ice cover is modeled as a thin elastic plate, and the bottom porosity is described by a real parameter. Using linear theory, the problem is formulated as an initial value problem for the velocity potential describing the motion. In the mathematical analysis, the Laplace and Hankel transform techniques have been used to obtain the depression of the ice-covered surface in the form of a multiple infinite integral. This integral is evaluated asymptotically by the method of stationary phase twice for a long time and a large distance from the origin. Simple numerical computations are performed to illustrate the effect of the ice-covered surface and bottom porosity on the surface elevation, phase velocity, and group velocity of the surface gravity waves. Mainly the far-field behavior of the progressive waves is observed in two different cases, namely initial depression and an impulse concentrated at the origin. From graphical representations, it is clearly visible that the presence of ice cover and a porous bottom decreases the wave amplitude. Due to the porous bottom, the amplitude of phase velocity decreases, whereas the amplitude of group velocity increases.

References:

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Memo

Memo:
Received date:2021-05-09;Accepted date:2021-10-09。
Corresponding author:Rumpa Chakraborty,E-mail:chak.rumpa@gmail.com
Last Update: 2022-03-21