### Abstract

Original language | Undefined |
---|---|

Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Number of pages | 31 |

Publication status | Published - Nov 2012 |

### Publication series

Name | Memorandum |
---|---|

Publisher | Department 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

*Inertial waves in a rectangular parallelepiped*. (Memorandum; No. 1998). Enschede: University of Twente, Department of Applied Mathematics.

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*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.

Research output: Book/Report › Report › Professional

TY - BOOK

T1 - Inertial waves in a rectangular parallelepiped

AU - Nurijanyan, S.

AU - Bokhove, Onno

AU - Maas, L.R.M.

PY - 2012/11

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.

KW - METIS-289791

KW - EWI-22540

KW - Rotating Fluids

KW - FEM discretisation

KW - Inertial waves

KW - IR-84370

M3 - Report

T3 - Memorandum

BT - Inertial waves in a rectangular parallelepiped

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

ER -