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  • Open Access

Common explanation for coherent patterns in transitional and turbulent wall-bounded flows

Yuxin Jiao*

  • *Contact author: y.jiao17@pku.edu.cn
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Phys. Rev. E 114, 045102 – Published 7 October, 2026

DOI: https://doi.org/10.1103/d1ps-ghh6

Abstract

A common explanation for selecting the shape and size of coherent patterns based on the filtering nature of the linearized Navier-Stokes equations is investigated. The filtering properties are examined by generalized optimal perturbations. Computing generalized optimal perturbations with different structure norms in a homogeneous shear flow demonstrates that different generalized optimal perturbations take different structural forms, implying the existence of multiple filtering properties of the linearized Navier-Stokes operators dependent on the filter output. Subsequently, linear simulations with random initial conditions are conducted to further clarify the capability of generalized optimal perturbations in representing the multiple filtering properties. With nonlinearity not taken into consideration, generalized optimal perturbations well predict the temporal evolutions of structural characteristics of multiple flow patterns governed by the linearized Navier-Stokes operators, thereby offering a more refined description of the multiple filtering properties than the optimal perturbation framework. The capability of generalized optimal perturbations in describing the filtering nature of the linearized Navier-Stokes operators is further examined in real turbulence with nonlinearity taken into account. In addition to the spanwise streak spacing, comparing with the direct numerical simulation results reveals that the spanwise length scale of spanwise velocity patterns can also be well-captured by the corresponding generalized optimal perturbations. This supports the effectiveness and intuitiveness of generalized optimal perturbations in representing the selectivity of the linearized Navier-Stokes operators, which is essential in dictating some specific flow patterns in fully developed turbulence.

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Phys. Rev. E 114, 045102– Published 7 October, 2026
  • Received 25 September 2025
  • Revised 8 July 2026
  • Accepted 9 September 2026
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