Example of parametric resonance in a rotating flow

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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 languageEnglish
Pages (from-to)313-315
Number of pages3
JournalFluid Dynamics
Volume22
Issue number2
DOIs
Publication statusPublished - Mar 1987

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ASJC Scopus subject areas

  • Fluid Flow and Transfer Processes

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