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International Conference on Mathematics and Computing

ICMC 2018: Mathematics and Computing pp 174–185Cite as

Cauchy Poisson Problem for Water with a Porous Bottom

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Part of the book series: Communications in Computer and Information Science ((CCIS,volume 834))

Abstract

This paper is concerned with generation of surface waves in an ocean with porous bottom due to initial disturbances at free surface. Assuming linear theory the problem is formulated as an initial value problem for the velocity potential describing the motion in the fluid. Laplace transform in time and Fourier transform in space have been utilized in the mathematical analysis to obtain the form of the free surface in terms of an integral. This integral is then evaluated asymptotically for large time and distance by the method of stationary phase for prescribed initial disturbance at the free surface in the form of depression of the free surface or an impulse at the free surface concentrated at the origin. The form of the free surface is depicted graphically for these two types of initial conditions in a number of figures to demonstrate the effect of the porosity at the bottom.

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References

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Acknowledgments

The authors thank the reviewers for their comments to modify the paper in the present form. This work is carried out under CSIR research project No. 25(0253)/16/EMR-II.

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Authors and Affiliations

  1. Jadavpur University, Kolkata, 700032, India

    Piyali Kundu & Sudeshna Banerjea

  2. Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B.T. Road, Kolkata, 700108, India

    B. N. Mandal

Authors
  1. Piyali Kundu
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  2. Sudeshna Banerjea
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  3. B. N. Mandal
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Corresponding author

Correspondence to Piyali Kundu .

Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences, Indian Institute of Technology BHU, Varanasi, Uttar Pradesh, India

    Debdas Ghosh

  2. Haldia Institute of Technology, Haldia, India

    Debasis Giri

  3. University of Central Florida, Orlando, Florida, USA

    Ram N. Mohapatra

  4. Istanbul Commerce University, Istanbul, Turkey

    Ekrem Savas

  5. Kyushu University, Fukuoka, Japan

    Kouichi Sakurai

  6. Indian Institute of Technology (BHU), Varanasi, India

    L. P. Singh

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© 2018 Springer Nature Singapore Pte Ltd.

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Cite this paper

Kundu, P., Banerjea, S., Mandal, B.N. (2018). Cauchy Poisson Problem for Water with a Porous Bottom. In: Ghosh, D., Giri, D., Mohapatra, R., Savas, E., Sakurai, K., Singh, L. (eds) Mathematics and Computing. ICMC 2018. Communications in Computer and Information Science, vol 834. Springer, Singapore. https://doi.org/10.1007/978-981-13-0023-3_17

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  • DOI: https://doi.org/10.1007/978-981-13-0023-3_17

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-13-0022-6

  • Online ISBN: 978-981-13-0023-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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