A Study on Inviscid Flow with a Free Surface over an Undulating Bottom

Panda, Srikumar

doi:10.18869/acadpub.jafm.68.228.24794

Cited by 2 publications

(2 citation statements)

References 17 publications

(21 reference statements)

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“…Equating the coefficients of the similar powers of the parameter ε, two independent boundary value problems (BVP) for the zeroth order and the first order potential functions are obtained. Martha and Bora (2007) and Panda (2016) used similar kind of perturbation involving a small parameter ε to investigate the oblique water wave diffraction by an ocean bed having small undulation. There the parameter ε is a measure of smallness of the bottom undulation.…”

Section: Introductionmentioning

confidence: 99%

Interaction of Water Waves with Permeable Barrier using Galerkin Approximation

Gayen

Gupta

2020

JAFM

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In this paper we analyze the interaction of water waves with a permeable barrier which is slightly perturbed from its vertical position within the framework of linearised water wave theory. The barrier is placed in water of finite depth. Two different kinds of barriers are examined, namely, (I) a partially immersed barrier and (II) a submerged bottom standing barrier. The governing boundary value problem involving the velocity potential function is split into two boundary value problems involving the zeroth order as well as the first order velocity potential functions by using a simplified perturbation technique. The zeroth order reflection and transmission coefficients which are due to a vertical permeable barrier are evaluated by solving a Fredholm integral equation of second kind numerically by using a one term Galerkin approximation. Green's theorem is applied to evaluate the first order reflection and transmission coefficients. The first order transmission coefficient vanishes irrespective of the shape of the barrier. The numerical values for the first order reflection coefficient are determined by choosing some appropriate shape functions. The numerical results for the zeroth order reflection coefficient which stand for the case of a vertical barrier are validated against the known results for both the permeable and impermeable barriers. The first order reflection curves are also compared by making the porosity constant to be zero with those available in the literature for an impermeable nearly vertical barrier.

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Section: Introductionmentioning

confidence: 99%

Interaction of Water Waves with Permeable Barrier using Galerkin Approximation

Gayen

Gupta

2020

JAFM

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“…Free-surface problems occur in many aspects of science and engineering. They can be defined as problems whose mathematical formulation involves surfaces that have to be found as part of the solution; for some recent development on the topic (see [1][2][3][4][5][6]) and the references therein. In this literature, we show some contributions of researchers to the finding of a mathematical solution for free-surface problems.…”

Section: Introductionmentioning

confidence: 99%