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 Smrutiranjan Mohapatra.The Interaction of Oblique Flexural Gravity Waves With a Small Bottom Deformation on a Porous Ocean-Bed: Green’s Function Approach[J].Journal of Marine Science and Application,2016,(2):112-122.[doi:10.1007/s11804-016-1353-y]
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The Interaction of Oblique Flexural Gravity Waves With a Small Bottom Deformation on a Porous Ocean-Bed: Green’s Function Approach


The Interaction of Oblique Flexural Gravity Waves With a Small Bottom Deformation on a Porous Ocean-Bed: Green’s Function Approach
Smrutiranjan Mohapatra
Smrutiranjan Mohapatra
Department of Mathematics, Veer Surendra Sai University of Technology, Burla 768018, India
oblique incident wavesbottom deformationporous bedelastic plateGreen’s functionreflection coefficienttransmission coefficientenergy identity
The interaction of oblique incident water waves with a small bottom deformation on a porous ocean-bed is examined analytically here within the framework of linear water wave theory. The upper surface of the ocean is assumed to be covered by an infinitely extended thin uniform elastic plate, while the lower surface is bounded by a porous bottom surface having a small deformation. By employing a simplified perturbation analysis, involving a small parameter δ(<<1), which measures the smallness of the deformation, the governing Boundary Value Problem (BVP) is reduced to a simpler BVP for the first-order correction of the potential function. This BVP is solved using a method based on Green’s integral theorem with the introduction of suitable Green’s function to obtain the first-order potential, and this potential function is then utilized to calculate the first-order reflection and transmission coefficients in terms of integrals involving the shape function c(x) representing the bottom deformation. Consideration of a patch of sinusoidal ripples shows that when the quotient of twice the component of the incident field wave number propagating just below the elastic plate and the ripple wave number approaches one, the theory predicts a resonant interaction between the bed and the surface below the elastic plate. Again, for small angles of incidence, the reflected wave energy is more as compared to the other angles of incidence. It is also observed that the reflected wave energy is somewhat sensitive to the changes in the flexural rigidity of the elastic plate, the porosity of the bed and the ripple wave numbers. The main advantage of the present study is that the results for the values of reflection and transmission coefficients obtained are found to satisfy the energy-balance relation almost accurately.


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Received date: 2015-07-28;Accepted date: 2015-12-23。
Foundation item: Partially Supported by a Research from Department of Science and Technology (DST), India under Grant No. SB/FTP/MS-003/2013
Corresponding author: Smrutiranjan Mohapatra,E-mail:smrutiranjan.m@gmail.com
Last Update: 2016-07-06