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Cauchy-poisson problem for a two-layer fluid with an inertial surface

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Abstract

This paper is concerned with the generation of waves due to initial disturbances at the upper surface of a two-layer fluid, as the upper layer is covered by an inertial surface and the lower layer extends infinitely downwards. The inertial surface is composed of thin but uniform distribution of non-interacting material. In the mathematical analysis, the Fourier and Laplace transform techniques have been utilized to obtain the depressions of the inertial surface and the interface in the form of infinite integrals. For initial disturbances concentrated at a point, the inertial surface depression and the interface depression are evaluated asymptotically for large time and distance by using the method of stationary phase. They are also depicted graphically for two types of initial disturbances and appropriate conclusions are made.

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References

  • Chaudhuri K (1968). Waves in shallow water due to arbitrary surface disturbances. Applied Scientific Research, 19(1), 274–284.

    Article  MATH  Google Scholar 

  • Dolai DP (1996). Waves produced by disturbances at the interface between two superposed fluids. Proceedings of the Indian National Science Academy, 62, 137–147.

    MATH  Google Scholar 

  • Dolai DP, Banerjea S (1997). On gravity-capillary waves due to interface disturbance. International Journal of Mathematical Education in Science and Technology, 28(1), 75–83.

    Article  MATH  Google Scholar 

  • Ghosh P, Basu U, Mandal BN (2000). Waves due to initial disturbances at the inertial surface in a stratified fluid of finite depth. International Journal of Mathematics and Mathematical Sciences, 24(4), 265–276.

    Article  MathSciNet  MATH  Google Scholar 

  • Ghosh P (2000), Waves due to initial axisymmetric disturbances at the inertial interface between two superposed fluids. Indian Journal of Pure and Applied Mathematics, 31(9), 1123–1133.

    MATH  Google Scholar 

  • Kranzer HC and Keller JB (1959). Water waves produced by explosions. Journal of Applied Physics, 30(3), 398–407.

    Article  MathSciNet  MATH  Google Scholar 

  • Lamb H (1916). On waves due to a travelling disturbance, with an application to waves in superposed fluids. Philosophical Magazine, Series 6, 31(184), 386–399.

    Article  MATH  Google Scholar 

  • Lamb H (1945). Hydrodynamics. Dover, New York.

    Google Scholar 

  • Lu DQ, Dai SQ (2008). Generation of unsteady waves by concentrated disturbances in an inviscid fluid with an inertial surface. Acta Mechanica Sinica, 24(3), 267–275.

    Article  MATH  Google Scholar 

  • Mandal BN (1988). Water waves generated by disturbance at an inertial surface. Applied Scientific Research, 45(1), 67–73.

    Article  MATH  Google Scholar 

  • Mandal BN, Mukherjee S (1989). Water waves generated at an inertial surface by an axisymmetric initial surface disturbance. International Journal of Mathematical Education in Science and Technology, 20(5), 743–747.

    Article  MATH  Google Scholar 

  • Maiti P, Mandal BN (2005a). Water waves generated by disturbances at an ice-cover. International Journal of Mathematics and Mathematical Sciences, (5), 737–746.

    Article  MathSciNet  Google Scholar 

  • Maiti P, Mandal BN (2005b). Water waves generated due to initial axis symmetric disturbances in water with an ice-cover. Archive. of Applied Mechanics, 74(9), 629–636.

    Article  MATH  Google Scholar 

  • Stoker JJ (1957). Water waves: the mathematical theory with applications. Interscience Publishers, Inc., New York, 149–187.

    MATH  Google Scholar 

  • Wen SL (1982). A note on water waves created by surface disturbances. International Journal of Mathematical Education in Science and Technology, 13(1), 55–58.

    Article  MATH  Google Scholar 

  • Zhevandrov PN, Isakov RV (1990). Cauchy-Poisson problem for a two-layer fluid of variable depth. Mathematical Notes, 47(6), 546–556.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

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

    Harpreet Dhillon

  2. NASI Senior Scientist, Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata, 700108, India

    B. N. Mandal

Authors
  1. Harpreet Dhillon
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  2. B. N. Mandal
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Corresponding author

Correspondence to B. N. Mandal.

Additional information

Foundation item: Supported by the DST Research Project No. SR/SY/MS: 521/08 and CSIR, New Delhi.

Harpreet Dhillon was born in 1986. She is working as a Junior Research Fellow in the Department of Mathematics, Jadavpur University, Kolkata, India. Her current research interests include water wave problems.

B.N. Mandal was born in 1943. He is a NASI Platinum Jubilee Senior Scientist in the Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata, India. His current research interests include water wave problems and associated mathematical techniques, Integral equations, Integral expansions, etc.

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Dhillon, H., Mandal, B.N. Cauchy-poisson problem for a two-layer fluid with an inertial surface. J. Marine. Sci. Appl. 12, 21–30 (2013). https://doi.org/10.1007/s11804-013-1163-z

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  • DOI: https://doi.org/10.1007/s11804-013-1163-z

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