Inertial waves in a rectangular parallelepiped

S. Nurijanyan, Onno Bokhove, L.R.M. Maas

    Research output: Book/ReportReportProfessional

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    Abstract

    A study of inertial gyroscopic waves in a rotating homogeneous fluid is undertaken both theoretically and numerically. A novel approach is presented to construct a semi-analytical solution of a linear three-dimensional fluid flow in a rotating rectangular parallelepiped bounded by solid walls. The three-dimensional solution is expanded in vertical modes to reduce the dynamics to the horizontal plane. On this horizontal plane the two dimensional solution is constructed via superposition of 'inertial' analogs of surface Poincar\'{e} and Kelvin waves reflecting from the walls. The infinite sum of inertial Poincar\'{e} waves has to cancel the normal flow of two inertial Kelvin waves near the boundaries. The wave system corresponding to every vertical mode results in an eigenvalue problem. Corresponding computations for rotationally modified surface gravity waves are in agreement with numerical values obtained by Taylor (1921), Rao (1966) and also, for inertial waves, by Maas (2003) upon truncation of an infinite matrix. The present approach enhances the currently available, structurally concise modal solution introduced by Maas (2003). In contrast to Maas' approach, our solution does not have any convergence issues in the interior and does not suffer from Gibbs phenomenon at the boundaries. Additionally, an alternative finite element method is used to contrast these two semi-analytical solutions with a purely numerical one. The main differences are discussed for a particular example and one eigenfrequency.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Number of pages31
    Publication statusPublished - Nov 2012

    Publication series

    NameMemorandum
    PublisherDepartment of Applied Mathematics, University of Twente
    No.1998
    ISSN (Print)1874-4850
    ISSN (Electronic)1874-4850

    Keywords

    • METIS-289791
    • EWI-22540
    • Rotating Fluids
    • FEM discretisation
    • Inertial waves
    • IR-84370

    Cite this

    Nurijanyan, S., Bokhove, O., & Maas, L. R. M. (2012). Inertial waves in a rectangular parallelepiped. (Memorandum; No. 1998). Enschede: University of Twente, Department of Applied Mathematics.
    Nurijanyan, S. ; Bokhove, Onno ; Maas, L.R.M. / Inertial waves in a rectangular parallelepiped. Enschede : University of Twente, Department of Applied Mathematics, 2012. 31 p. (Memorandum; 1998).
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    abstract = "A study of inertial gyroscopic waves in a rotating homogeneous fluid is undertaken both theoretically and numerically. A novel approach is presented to construct a semi-analytical solution of a linear three-dimensional fluid flow in a rotating rectangular parallelepiped bounded by solid walls. The three-dimensional solution is expanded in vertical modes to reduce the dynamics to the horizontal plane. On this horizontal plane the two dimensional solution is constructed via superposition of 'inertial' analogs of surface Poincar\'{e} and Kelvin waves reflecting from the walls. The infinite sum of inertial Poincar\'{e} waves has to cancel the normal flow of two inertial Kelvin waves near the boundaries. The wave system corresponding to every vertical mode results in an eigenvalue problem. Corresponding computations for rotationally modified surface gravity waves are in agreement with numerical values obtained by Taylor (1921), Rao (1966) and also, for inertial waves, by Maas (2003) upon truncation of an infinite matrix. The present approach enhances the currently available, structurally concise modal solution introduced by Maas (2003). In contrast to Maas' approach, our solution does not have any convergence issues in the interior and does not suffer from Gibbs phenomenon at the boundaries. Additionally, an alternative finite element method is used to contrast these two semi-analytical solutions with a purely numerical one. The main differences are discussed for a particular example and one eigenfrequency.",
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    author = "S. Nurijanyan and Onno Bokhove and L.R.M. Maas",
    year = "2012",
    month = "11",
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    series = "Memorandum",
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    Nurijanyan, S, Bokhove, O & Maas, LRM 2012, Inertial waves in a rectangular parallelepiped. Memorandum, no. 1998, University of Twente, Department of Applied Mathematics, Enschede.

    Inertial waves in a rectangular parallelepiped. / Nurijanyan, S.; Bokhove, Onno; Maas, L.R.M.

    Enschede : University of Twente, Department of Applied Mathematics, 2012. 31 p. (Memorandum; No. 1998).

    Research output: Book/ReportReportProfessional

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    T1 - Inertial waves in a rectangular parallelepiped

    AU - Nurijanyan, S.

    AU - Bokhove, Onno

    AU - Maas, L.R.M.

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    Y1 - 2012/11

    N2 - A study of inertial gyroscopic waves in a rotating homogeneous fluid is undertaken both theoretically and numerically. A novel approach is presented to construct a semi-analytical solution of a linear three-dimensional fluid flow in a rotating rectangular parallelepiped bounded by solid walls. The three-dimensional solution is expanded in vertical modes to reduce the dynamics to the horizontal plane. On this horizontal plane the two dimensional solution is constructed via superposition of 'inertial' analogs of surface Poincar\'{e} and Kelvin waves reflecting from the walls. The infinite sum of inertial Poincar\'{e} waves has to cancel the normal flow of two inertial Kelvin waves near the boundaries. The wave system corresponding to every vertical mode results in an eigenvalue problem. Corresponding computations for rotationally modified surface gravity waves are in agreement with numerical values obtained by Taylor (1921), Rao (1966) and also, for inertial waves, by Maas (2003) upon truncation of an infinite matrix. The present approach enhances the currently available, structurally concise modal solution introduced by Maas (2003). In contrast to Maas' approach, our solution does not have any convergence issues in the interior and does not suffer from Gibbs phenomenon at the boundaries. Additionally, an alternative finite element method is used to contrast these two semi-analytical solutions with a purely numerical one. The main differences are discussed for a particular example and one eigenfrequency.

    AB - A study of inertial gyroscopic waves in a rotating homogeneous fluid is undertaken both theoretically and numerically. A novel approach is presented to construct a semi-analytical solution of a linear three-dimensional fluid flow in a rotating rectangular parallelepiped bounded by solid walls. The three-dimensional solution is expanded in vertical modes to reduce the dynamics to the horizontal plane. On this horizontal plane the two dimensional solution is constructed via superposition of 'inertial' analogs of surface Poincar\'{e} and Kelvin waves reflecting from the walls. The infinite sum of inertial Poincar\'{e} waves has to cancel the normal flow of two inertial Kelvin waves near the boundaries. The wave system corresponding to every vertical mode results in an eigenvalue problem. Corresponding computations for rotationally modified surface gravity waves are in agreement with numerical values obtained by Taylor (1921), Rao (1966) and also, for inertial waves, by Maas (2003) upon truncation of an infinite matrix. The present approach enhances the currently available, structurally concise modal solution introduced by Maas (2003). In contrast to Maas' approach, our solution does not have any convergence issues in the interior and does not suffer from Gibbs phenomenon at the boundaries. Additionally, an alternative finite element method is used to contrast these two semi-analytical solutions with a purely numerical one. The main differences are discussed for a particular example and one eigenfrequency.

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    KW - FEM discretisation

    KW - Inertial waves

    KW - IR-84370

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    BT - Inertial waves in a rectangular parallelepiped

    PB - University of Twente, Department of Applied Mathematics

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    Nurijanyan S, Bokhove O, Maas LRM. Inertial waves in a rectangular parallelepiped. Enschede: University of Twente, Department of Applied Mathematics, 2012. 31 p. (Memorandum; 1998).