ICMC 2018: Mathematics and Computing pp 174-185

# Cauchy Poisson Problem for Water with a Porous Bottom

Conference paper
Part of the Communications in Computer and Information Science book series (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.

## Keywords

Cauchy Poisson problem Porous bottom Laplace and Fourier transform Method of stationary phase Free surface depression

## Notes

### 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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© Springer Nature Singapore Pte Ltd. 2018

## Authors and Affiliations

• Piyali Kundu
• 1
• Sudeshna Banerjea
• 1
• B. N. Mandal
• 2