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Subcritical transitional flow in two-dimensional plane Poiseuille flow

Published online by Cambridge University Press:  18 September 2024

Z. Huang Open the ORCID record for Z. Huang [Opens in a new window] ,
R. Gao ,
Y.Y. Gao  and
G. Xi
Z. Huang
Affiliation:
Department of Fluid Machinery and Engineering, Xi'an Jiaotong University, Xi'an 710049, PR China
R. Gao
Affiliation:
Department of Fluid Machinery and Engineering, Xi'an Jiaotong University, Xi'an 710049, PR China
Y.Y. Gao
Affiliation:
Department of Fluid Machinery and Engineering, Xi'an Jiaotong University, Xi'an 710049, PR China
G. Xi*
Affiliation:
Department of Fluid Machinery and Engineering, Xi'an Jiaotong University, Xi'an 710049, PR China
*
†Email address for correspondence: xiguang@mail.xjtu.edu.cn
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Abstract

Recently, subcritical transition to turbulence in the quasi-two-dimensional (quasi-2-D) shear flow with strong linear friction (Camobreco et al., J. Fluid Mech., vol. 963, 2023, R2) has been demonstrated by the 2-D mechanism at $Re = 71\,211$, and the nonlinear Tollmien–Schlichting (TS) waves related to the edge state were approached independently of initial optimal disturbances. For 2-D plane Poiseuille flow, transition to the fully developed turbulence requires that the Reynolds number is several times larger than the critical Reynolds number $Re_c$ (Markeviciute & Kerswell, J. Fluid Mech., vol. 917, 2021, A57). In this paper, we observed the subcritical transitional flow in 2-D plane Poiseuille flow driven by the nonlinear TS waves by both linear and nonlinear optimal disturbances ($Re < Re_c$) with different quantitative edge states. The nonlinear optimal disturbances could trigger the sustained subcritical transitional flow for $Re \geqslant 2400$. The initial energy for nonlinear optimal disturbance is more efficient than the linear optimal disturbance in reaching the subcritical transitional flow for $2400 \leqslant Re \leqslant 5000$. Moreover, the initial energy of linear optimal disturbance is larger than the energy of its edge state. The nonlinear TS waves along the edge state are formed by the nonlinear optimal disturbances to trigger transitional flow, which agrees well with the main conclusions of Camobreco et al. (J. Fluid Mech., vol. 963, 2023, R2), while the required $Re$ of 2-D plane Poiseuille flow is much smaller.

JFM classification

Instability: Nonlinear instability Instability: Shear-flow instability

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 994 , 10 September 2024 , A6
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© The Author(s), 2024. Published by Cambridge University Press

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