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Algebraic disturbances and their consequences in rotating channel flow transition

S. Jose¹, V. Kuzhimparampil¹, B. Pier² and R. Govindarajan³

¹Center for Interdisciplinary Sciences, Tata Institute of Fundamental Research, 21 Brundavan Colony, Narsingi, Hyderabad, 500075, India; ²Laboratoire de mécanique des fluides et d'acoustique, École centrale de Lyon – CNRS – Université Claude-Bernard Lyon 1 – INSA, 36 avenue Guy-de-Collongue, 69134 Écully cedex, France; ³International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Survey 151, Shivakote, Hesaraghatta Hobli, Bengaluru 560089, India

Physical Review Fluids 2, 083901 (25 pages) (2017)

Abstract:

It is now established that subcritical mechanisms play a crucial role in the transition to turbulence of non-rotating plane shear flows. The role of these mechanisms in rotating channel flow is examined here in the linear and nonlinear stages. Distinct patterns of behaviour are found: the transient growth leading to nonlinearity at low rotation rates Ro, a highly chaotic intermediate Ro regime, a localised weak chaos at higher Ro, and complete stabilization of transient disturbances at very high Ro. At very low Ro, the transient growth amplitudes are close to those for non-rotating flow, but Coriolis forces already assert themselves by producing distinct asymmetry about the channel centreline. Nonlinear processes are then triggered, in a streak-breakdown mode of transition. The high Ro regimes do not show these signatures, here the leading eigenmode emerges as dominant in the early stages. Elongated structures plastered close to one wall are seen at higher rotation rates. Rotation is shown to reduce non-normality in the linear operator, in an indirect manifestation of Taylor--Proudman effects. Although the critical Reynolds for exponential growth of instabilities is known to vary a lot with rotation rate, we show that the energy critical Reynolds number is insensitive to rotation rate. It is hoped that these findings will motivate experimental verification, and examination of other rotating flows in this light.

doi:10.1103/PhysRevFluids.2.083901

hal-01578604

2017b_jose_prf.pdf

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