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Zh. Vychisl. Mat. Mat. Fiz., 2019, Volume 59, Number 6, Pages 1024–1036 (Mi zvmmf10912)  

Emergence of self-excited oscillations in flows of inviscid fluids in a channel

V. N. Govorukhin

Southern Federal University, Rostov-on-Don, 344090 Russia

Abstract: The mechanism of self-excited oscillations arising in an ideal incompressible fluid flowing through a rectangular channel is studied numerically. The problem is formulated in the form of the Euler equations for ideal fluid dynamics in terms of vorticity and stream function with Yudovich's boundary conditions. The vorticity intensity at the inlet of the channel is used as a bifurcation parameter. Grid approximations are employed to search for steady-state regimes and to analyze their stability, while the nonstationary problem is solved by applying the vortex-in-cell method. It is shown that a steady flow through the channel is established when the vorticity intensity at the inlet is low. As the vorticity intensity at the inlet grows, the steady-state regime becomes unstable in an oscillatory manner and self-excited oscillations emerge in its neighborhood. The evolution of the self-excited oscillations with an increasing bifurcation parameter is studied. In the case of high supercriticality, a chaotic flow regime is observed in the channel.

Key words: ideal fluid, channel flow, self-excited oscillations, stability.

DOI: https://doi.org/10.1134/S0044466919060073


English version:
Computational Mathematics and Mathematical Physics, 2019, 59:6, 994–1005

Bibliographic databases:

UDC: 519.634
Received: 20.12.2018
Revised: 20.12.2018
Accepted:08.02.2019

Citation: V. N. Govorukhin, “Emergence of self-excited oscillations in flows of inviscid fluids in a channel”, Zh. Vychisl. Mat. Mat. Fiz., 59:6 (2019), 1024–1036; Comput. Math. Math. Phys., 59:6 (2019), 994–1005

Citation in format AMSBIB
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\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2019
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\issue 6
\pages 1024--1036
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\pages 994--1005
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