### Abstract

Parametric resonance is one of the common types of instability of mechanical systems [1]. A standard example of the equations describing parametric oscillations is the Mathieu equation and its generalizations. In hydrodynamics these oscillations have been closely studied in connection with the problem of the vertical oscillations of a vessel containing an incompressible fluid in a uniform gravity field [1-5]. In this paper a new example of a flow whose stability problem reduces to the Mathieu equation is given. This is a flow of special type in a rotating cylindrical channel. The direction of the angular velocity is perpendicular to the channel axis, and its magnitude varies periodically with time. Flows with this geometry are of potential interest in technical applications [6, 7].

Original language | English |
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Pages (from-to) | 313-315 |

Number of pages | 3 |

Journal | Fluid Dynamics |

Volume | 22 |

Issue number | 2 |

DOIs | |

Publication status | Published - Mar 1987 |

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### ASJC Scopus subject areas

- Fluid Flow and Transfer Processes

### Cite this

*Fluid Dynamics*,

*22*(2), 313-315. https://doi.org/10.1007/BF01052270

**Example of parametric resonance in a rotating flow.** / Vladimirov, V. A.

Research output: Contribution to journal › Article

*Fluid Dynamics*, vol. 22, no. 2, pp. 313-315. https://doi.org/10.1007/BF01052270

}

TY - JOUR

T1 - Example of parametric resonance in a rotating flow

AU - Vladimirov, V. A.

PY - 1987/3

Y1 - 1987/3

N2 - Parametric resonance is one of the common types of instability of mechanical systems [1]. A standard example of the equations describing parametric oscillations is the Mathieu equation and its generalizations. In hydrodynamics these oscillations have been closely studied in connection with the problem of the vertical oscillations of a vessel containing an incompressible fluid in a uniform gravity field [1-5]. In this paper a new example of a flow whose stability problem reduces to the Mathieu equation is given. This is a flow of special type in a rotating cylindrical channel. The direction of the angular velocity is perpendicular to the channel axis, and its magnitude varies periodically with time. Flows with this geometry are of potential interest in technical applications [6, 7].

AB - Parametric resonance is one of the common types of instability of mechanical systems [1]. A standard example of the equations describing parametric oscillations is the Mathieu equation and its generalizations. In hydrodynamics these oscillations have been closely studied in connection with the problem of the vertical oscillations of a vessel containing an incompressible fluid in a uniform gravity field [1-5]. In this paper a new example of a flow whose stability problem reduces to the Mathieu equation is given. This is a flow of special type in a rotating cylindrical channel. The direction of the angular velocity is perpendicular to the channel axis, and its magnitude varies periodically with time. Flows with this geometry are of potential interest in technical applications [6, 7].

UR - http://www.scopus.com/inward/record.url?scp=0023308145&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0023308145&partnerID=8YFLogxK

U2 - 10.1007/BF01052270

DO - 10.1007/BF01052270

M3 - Article

VL - 22

SP - 313

EP - 315

JO - Fluid Dynamics

JF - Fluid Dynamics

SN - 0015-4628

IS - 2

ER -