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Research Papers: Ocean Engineering

Forced Flexural Gravity Wave Motion in Two-Layer Fluid

[+] Author and Article Information
R. Mondal

Department of Ocean Engineering and
Naval Architecture,
Indian Institute of Technology Kharagpur,
Kharagpur 721302India;
Department of Ocean Technology Policy
and Environment,
Graduate School of Frontier Sciences,
University of Tokyo,
Kashiwa 277-8563, Japan
e-mail: ramnarayaniitkgp@gmail.com

J. Bhattacharjee

Department of Ocean Engineering and
Naval Architecture,
Indian Institute of Technology Kharagpur,
Kharagpur 721302, India
e-mail: joydip@naval.iitkgp.ernet.in

T. Sahoo

Department of Ocean Engineering and
Naval Architecture,
Indian Institute of Technology Kharagpur,
Kharagpur 721302, India
e-mails: tsahoo1967@gmail.com;
tsahoo@naval.iitkgp.ernet.in

1Corresponding author.

Contributed by the Ocean, Offshore, and Arctic Engineering Division of ASME for publication in the JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING. Manuscript received September 18, 2014; final manuscript received February 17, 2015; published online March 16, 2015. Assoc. Editor: Daniel T. Valentine.

J. Offshore Mech. Arct. Eng 137(3), 031101 (Jun 01, 2015) (12 pages) Paper No: OMAE-14-1130; doi: 10.1115/1.4029896 History: Received September 18, 2014; Revised February 17, 2015; Online March 16, 2015

Generation of flexural gravity waves in a two-layer fluid due to the forced motion of a vertical rigid wavemaker is studied in both finite and infinite water depths. The two-dimensional (2D) fluid domain having an interface is covered by a semi-infinite ice sheet, which is modeled as an elastic beam. As an application of the wavemaker problem, flexural gravity wave reflection by a vertical cliff is analyzed. Under the assumptions of small amplitude water wave theory and structural response, the mathematical models are solved using a recently developed expansion formulae and the associated orthogonal mode-coupling relations as appropriate for finite and infinite water depths. Effect of three types of edges such as free edge, simply supported edge, and built-in edge on the wave reflection by the vertical cliff is analyzed whilst, for the wavemaker, the floating ice sheet is assumed to have free edge. Effect of various physical parameters on the wave motion is studied by analyzing the reflection coefficients, deflection of the ice sheet, interface elevation, strain and shear force on the floating ice sheet.

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Figures

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Fig. 1

Schematic diagram: (a) finite depth and (b) infinite depth

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Fig. 2

Ice deflection for different edge conditions with ω = 0.5 s−1, h/H = 0.5, d = 1 m, N = 0

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Fig. 3

Interface elevation for different edge conditions with ω = 0.5 s−1, h/H = 0.5, d = 1 m, N = 0

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Fig. 4

Ice deflection for different thickness d with ω = 0.5 s−1, h/H = 0.5, N = 0

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Fig. 5

Ice deflection for different compressive force N with ω = 0.5 s−1, h/H = 0.5, d = 1 m

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Fig. 6

Ice deflection for different depth ratio h/H with ω = 1 s−1, d = 1 m, N = 0

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Fig. 7

Strain along ice sheet for different edge conditions with the parameters ω = 0.5 s−1 and h/H = 0.5, N = 0, d = 1 m

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Fig. 8

Strain along ice sheet for different density ratio s with ω = 0.5 s−1, h/H = 0.5, N = 0, d = 1 m

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Fig. 9

Strain along ice sheet for different ice thickness with ω = 0.5 s−1, h/H = 0.5, N = 0

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Fig. 10

Strain along ice sheet for different compressive force with ω = 0.5 s−1 and N = 0, d = 1 m

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Fig. 11

Shear force along ice sheet for different edge conditions with ω = 0.5 s−1 and h/H = 0.5, N = 0, d = 1 m

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Fig. 12

Shear force along ice sheet for different ice thickness with ω = 0.5 s−1, h/H = 0.5, N = 0

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Fig. 13

Shear force along ice sheet for different compressive force with ω = 0.5 s−1 and h/H = 0.5, d = 1 m

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Fig. 14

Shear force along ice sheet for different density ratio with ω = 0.5 s−1 and h/H = 0.5, d = 1 m

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Fig. 15

Ice deflection for different angular frequency with s−1 and h/H = 0.5, d = 1 m, s0 = 1 m

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Fig. 16

Interface elevation for different angular frequency with h/H = 0.5, d = 1 m, s0 = 1 m

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Fig. 17

Strain for different angular frequency with h/H = 0.5, d = 1 m, s0 = 1 m

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Fig. 18

Shear force for different angular frequency with and h/H = 0.5, d = 1 m, s0 = 1 m

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