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From oblique-wave forcing to streak reinforcement: A perturbation-based frequency-response framework

Dušan Božić1,*, Anubhav Dwivedi2,†, and Mihailo R. Jovanović1,‡

  • *Contact author: dbozic@usc.edu
  • †Contact author: anubhavd91@gmail.com
  • ‡Contact author: mihailo@usc.edu
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Phys. Rev. Fluids 11, 063901 – Published 4 June, 2026

DOI: https://doi.org/10.1103/sgrw-g148

Abstract

We develop a perturbation-based frequency-response framework for analyzing amplification mechanisms that are central to subcritical routes to transition in wall-bounded shear flows. By systematically expanding the input-output dynamics of fluctuations about the laminar base flow with respect to forcing amplitude, we establish a rigorous correspondence between linear resolvent analysis and higher-order nonlinear interactions. At second order, quadratic interactions of unsteady oblique waves generate steady streamwise streaks via the lift-up mechanism. We demonstrate that the spatial structure of these streaks is captured by the second output singular function of the streamwise-constant resolvent operator. At higher orders, nonlinear coupling between oblique waves and induced streaks acts as structured forcing of the laminar linearized dynamics, yielding additional streak components whose relative phase governs reinforcement or attenuation of the leading-order streak response. Our analysis identifies a critical forcing amplitude marking the breakdown of the weakly nonlinear regime, beyond which direct numerical simulations exhibit sustained unsteadiness. We show that this breakdown coincides with the onset of secondary instability, revealing that the nonlinear interactions responsible for streak formation also drive the modal growth central to classical transition theory. The resulting framework provides a mechanistically transparent and computationally efficient description of transition that unifies nonmodal amplification, streak formation, and modal instability within a single formulation derived directly from the Navier–Stokes equations.

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Outline

Information

Phys. Rev. Fluids 11, 063901– Published 4 June, 2026
  • Received 9 February 2026
  • Accepted 10 April 2026
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