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Waves Generated on Running Stream due to a Disturbance on Sea Bed

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Abstract

In this paper we have studied the effect of running stream on the waves generated by disturbance on the sea bed. The problem is formulated as an initial cum boundary value problem with Laplace equation as the governing differential equation. Employing Laplace transform in time and Fourier transform in space, the free surface depression is obtained which is then evaluated asymptotically at a large distance and after a long time after the occurrence of the disturbance.The asymptotic form of the free surface depression is studied graphically for different values of the parameter. It is observed that in absence of running stream, the free surface depression exhibits uniform oscillatory behaviour at large distance from the occurrence of the disturbance and also after a long lapse of time. However in the presence of the uniform current it is found that if the velocity of the running stream is less than a critical value then there occurs an interaction between the wave and the stream due to which there is a significant change in the asymptotic form of free surface depression.

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Acknowledgements

PK acknowledges CSIR for financial support through Fellowship Award No. 09/096(0979)/2019-EMRI. SB and PM acknowledge SERB for financial support through research schemes (Matrics MTR/2017/000363 and EMR/2016/005315, respectively).

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Authors and Affiliations

  1. Department of Mathematics, Jadavpur University, Kolkata, 700032, India

    Piyali Kundu, Jiteshwar Chatterjee & Sudeshna Banerjea

  2. Calcutta University, Technology Campus, JB 2, Sector III, Kolkata, 700098, India

    Paramita Maiti

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  1. Piyali Kundu
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  2. Jiteshwar Chatterjee
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  3. Sudeshna Banerjea
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  4. Paramita Maiti
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Correspondence to Sudeshna Banerjea.

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Kundu, P., Chatterjee, J., Banerjea, S. et al. Waves Generated on Running Stream due to a Disturbance on Sea Bed. Int. J. Appl. Comput. Math 6, 39 (2020). https://doi.org/10.1007/s40819-020-0793-x

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  • DOI: https://doi.org/10.1007/s40819-020-0793-x

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