Predicting trigger in streak breakdown via Picard-Chebyshev approach in plane-Poiseuille flow

Abstract

The evolution of finite-amplitude disturbances is critical in the prediction of laminar-to-turbulent transition. To analyze the transient growth of disturbances, Pralits et al. (J. Fluid Mechanics, 2015) proposed a weakly nonlinear optimal perturbation (WNLOP) analysis that accounts for the effect of mean-flow distortion on the fundamental wave. The present study formulates a WNLOP analysis via Picard--Chebyshev iteration for compressible parallel flows to predict streak breakdown. The formulation incorporates the non-modal amplification of disturbances and their nonlinear interactions for polychromatic waves, considering all the possible nonlinear interactions starting from a finite set of initial wavenumber components. The nonlinear interaction is tracked as a monotonically increasing set of wavenumber components; specifically, the first-order approximation recovers the linear disturbance equation, the third-order approximation corresponds to the amplitude equation of weakly nonlinear theory, and further iterations systematically approach DNS results in the weakly nonlinear regime. By applying the proposed formulation to a subcritical plane Poiseuille flow at Mach number M=0.3 and Reynolds number Re=3000, the proposed formulation demonstrates high predictive accuracy in comparison with DNS calculations and succeeds in identifying the optimal perturbation restricted to a planar wave that causes streak breakdown in full nonlinear simulation. The proposed method predicts the nonlinear interaction between the streak and the planar wave, which generates an oblique wave and subsequent harmonic waves characterized by an alternating streamwise vortex structure, whose amplitude determines whether further nonlinear interactions are induced to trigger the turbulent transition.

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BibTeX RIS

BibTeX

@misc{taniguchi2026predicting,
  title = {{Predicting trigger in streak breakdown via Picard-Chebyshev approach in plane-Poiseuille flow}},
  author = {Nobutaka Taniguchi and Aiko Yakeno},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.27475},
  eprint = {2610.27475},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.27475},
}

RIS

TY  - UNPB
TI  - Predicting trigger in streak breakdown via Picard-Chebyshev approach in plane-Poiseuille flow
AU  - Nobutaka Taniguchi
AU  - Aiko Yakeno
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2610.27475
UR  - https://arxiv.org/abs/2610.27475
AB  - The evolution of finite-amplitude disturbances is critical in the prediction of laminar-to-turbulent transition. To analyze the transient growth of disturbances, Pralits et al. (J. Fluid Mechanics, 2015) proposed a weakly nonlinear optimal perturbation (WNLOP) analysis that accounts for the effect of mean-flow distortion on the fundamental wave. The present study formulates a WNLOP analysis via Picard--Chebyshev iteration for compressible parallel flows to predict streak breakdown. The formulation incorporates the non-modal amplification of disturbances and their nonlinear interactions for polychromatic waves, considering all the possible nonlinear interactions starting from a finite set of initial wavenumber components. The nonlinear interaction is tracked as a monotonically increasing set of wavenumber components; specifically, the first-order approximation recovers the linear disturbance equation, the third-order approximation corresponds to the amplitude equation of weakly nonlinear theory, and further iterations systematically approach DNS results in the weakly nonlinear regime. By applying the proposed formulation to a subcritical plane Poiseuille flow at Mach number M=0.3 and Reynolds number Re=3000, the proposed formulation demonstrates high predictive accuracy in comparison with DNS calculations and succeeds in identifying the optimal perturbation restricted to a planar wave that causes streak breakdown in full nonlinear simulation. The proposed method predicts the nonlinear interaction between the streak and the planar wave, which generates an oblique wave and subsequent harmonic waves characterized by an alternating streamwise vortex structure, whose amplitude determines whether further nonlinear interactions are induced to trigger the turbulent transition.
ER  -

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