Non-linear oscillations of fluid in a container

J.H.G. Verhagen, L. van Wijngaarden

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Abstract

This paper is concerned with forced oscillations of fluid in a rectangular container. From the linearized approximation of the equations governing these oscillations, resonance frequencies are obtained for which the amplitude of the oscillations becomes infinite. Observation shows that under these circumstances a hydraulic jump is formed, which travels periodically back and forth between the walls of the container. This hydraulic jump is a non-linear phenomenon, analogous to the shock wave appearing in one-dimensional gas flow under similar resonance conditions. A theory developed by previous authors for one-dimensional gas flow is applied to the fluid oscillations in order to calculate the strength and the phase of the jump. The moment exerted on the container is also calculated. These quantities were measured experimentally at the lowest resonance frequency and the results are in good agreement with the theoretical values.
Original languageEnglish
Pages (from-to)737-751
JournalJournal of fluid mechanics
Volume22
Issue number4
DOIs
Publication statusPublished - 1965

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containers
Hydraulic jump
Containers
hydraulics
oscillations
gas flow
Fluids
Flow of gases
fluids
forced vibration
Shock waves
travel
shock waves
moments
approximation

Cite this

Verhagen, J.H.G. ; van Wijngaarden, L. / Non-linear oscillations of fluid in a container. In: Journal of fluid mechanics. 1965 ; Vol. 22, No. 4. pp. 737-751.
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Non-linear oscillations of fluid in a container. / Verhagen, J.H.G.; van Wijngaarden, L.

In: Journal of fluid mechanics, Vol. 22, No. 4, 1965, p. 737-751.

Research output: Contribution to journalArticleAcademic

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AU - Verhagen, J.H.G.

AU - van Wijngaarden, L.

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AB - This paper is concerned with forced oscillations of fluid in a rectangular container. From the linearized approximation of the equations governing these oscillations, resonance frequencies are obtained for which the amplitude of the oscillations becomes infinite. Observation shows that under these circumstances a hydraulic jump is formed, which travels periodically back and forth between the walls of the container. This hydraulic jump is a non-linear phenomenon, analogous to the shock wave appearing in one-dimensional gas flow under similar resonance conditions. A theory developed by previous authors for one-dimensional gas flow is applied to the fluid oscillations in order to calculate the strength and the phase of the jump. The moment exerted on the container is also calculated. These quantities were measured experimentally at the lowest resonance frequency and the results are in good agreement with the theoretical values.

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