Interaction of Water Waves with Permeable Barrier using Galerkin Approximation Article Swipe
R. Gayen
,
Sumanta Gupta
·
YOU?
·
· 2019
· Open Access
·
· DOI: https://doi.org/10.29252/jafm.13.01.29877
YOU?
·
· 2019
· Open Access
·
· DOI: https://doi.org/10.29252/jafm.13.01.29877
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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- Type
- article
- Language
- en
- Landing Page
- http://doi.org/10.29252/jafm.13.01.29877
- https://doi.org/10.29252/jafm.13.01.29877
- OA Status
- diamond
- Cited By
- 1
- References
- 33
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W2970123607
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- OpenAlex ID
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https://openalex.org/W2970123607Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.29252/jafm.13.01.29877Digital Object Identifier
- Title
-
Interaction of Water Waves with Permeable Barrier using Galerkin ApproximationWork title
- Type
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articleOpenAlex work type
- Language
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enPrimary language
- Publication year
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2019Year of publication
- Publication date
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2019-09-01Full publication date if available
- Authors
-
R. Gayen, Sumanta GuptaList of authors in order
- Landing page
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https://doi.org/10.29252/jafm.13.01.29877Publisher landing page
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https://doi.org/10.29252/jafm.13.01.29877Direct link to full text PDF
- Open access
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YesWhether a free full text is available
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-
diamondOpen access status per OpenAlex
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https://doi.org/10.29252/jafm.13.01.29877Direct OA link when available
- Concepts
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Galerkin method, Mechanics, Environmental science, Physics, Materials science, Thermodynamics, Finite element methodTop concepts (fields/topics) attached by OpenAlex
- Cited by
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1Total citation count in OpenAlex
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2021: 1Per-year citation counts (last 5 years)
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33Number of works referenced by this work
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.coefficients. | 141 |
| abstract_inverted_index.approximation. | 128 |
| cited_by_percentile_year.max | 93 |
| cited_by_percentile_year.min | 89 |
| countries_distinct_count | 1 |
| institutions_distinct_count | 2 |
| sustainable_development_goals[0].id | https://metadata.un.org/sdg/6 |
| sustainable_development_goals[0].score | 0.7799999713897705 |
| sustainable_development_goals[0].display_name | Clean water and sanitation |
| citation_normalized_percentile.value | 0.53272001 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |