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    The 62nd Annual Meeting of the Australian Mathematical Society (AustMS 2018)

    Ermakov, Andrei (2018) The 62nd Annual Meeting of the Australian Mathematical Society (AustMS 2018). In: Mathematical problems of long wave transformation in a coastal zone with a variable bathymetry, 4-7 December 2018, University of Adelaide, Australia.

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    We apply the rigorous mathematical methods to investigate surface wave transformation in a basin with a variable bathymetry. The development of rigorous mathematical methods for the description of wave transformation in the coastal zone represents an important and topical problem both from the academic and practical points of view, especially in the application of the protection of the Australian coastline from the hazardous impacts of oceanic waves. We consider long linear wave transformations in a coastal zone where water depth can vary arbitrarily smoothly. The derived system of differential equations that describes the changes of wave speed and free surface elevation are solved exactly for the different types of bottom profile. New analytical solutions in terms of special functions for wave transformation were obtained. The transformation coefficients were derived as the functions of wave frequency and the total depth drop for three typical models: piece-linear, piecequadratic, and hyperbolic tangential depth profiles. For all these cases we have derived exactly solvable equations and obtained their solutions in terms of hypergeometric functions. The influence of the governing parameters on the type of wave transformation was analysed. We show that the results obtained are in agreement with the energy flux conservation and Lamb's formula in the limiting case of zero frequency.

    Item Type: Conference or Workshop Item (Other)
    Keywords: Australian Mathematical Society; AustMS 2018;
    Academic Unit: Faculty of Science and Engineering > Electronic Engineering
    Item ID: 16659
    Depositing User: Dr Andrei Ermakov
    Date Deposited: 07 Nov 2022 10:57
    Refereed: Yes
    Use Licence: This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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