Effects of Spanwise Curvature on Hypersonic Boundary Layer Transition in Görtler-driven Flows

Abstract

The influence of spanwise convex curvature on hypersonic boundary-layer transition over a streamwise-concave surface is investigated using direct numerical simulation and Mach 7 experiments. Smooth doubly curved geometries with fixed streamwise concavity and increasing spanwise convex curvature isolate the effects of three-dimensional wall curvature on a centrifugally unstable boundary layer. Increasing spanwise curvature delays transition while preserving a Gortler-dominated route to breakdown. As spanwise curvature increases, the boundary layer thins, reducing the effective Görtler number and weakening centrifugal amplification of streamwise vortices. Consequently, growth of the primary Görtler instability is reduced, vortical structures remain closer to the wall, and secondary instability and turbulent breakdown shift downstream. Spectral proper orthogonal decomposition confirms that low-frequency vortical dynamics remain dominant in controlling transition, with sinuous secondary instability of Görtler vortices providing the principal route to breakdown. Meanwhile, boundary-layer thinning modifies acoustic instability dynamics: the second Mack mode shifts to higher frequencies and higher-frequency supersonic disturbances become increasingly prominent near breakdown as spanwise curvature increases. These acoustic disturbances remain subdominant and do not replace the Görtler-sinuous mechanism as the primary transition pathway. Numerical and experimental results exhibit consistent trends in transition location, thermal-streak organisation and disturbance evolution, supporting a common physical interpretation. These findings demonstrate that spanwise convex curvature stabilises hypersonic Görtler-dominated boundary layers, primarily by suppressing centrifugal amplification and delaying secondary instability, while leaving the transition pathway qualitatively unchanged.

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BibTeX RIS

BibTeX

@misc{welter2026effects,
  title = {{Effects of Spanwise Curvature on Hypersonic Boundary Layer Transition in Görtler-driven Flows}},
  author = {Andrew Welter and Ngoc Cuong Nguyen and Nicholas Webber and Mark Gragston and Jaime Peraire and Wesley Harris},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.23754},
  eprint = {2610.23754},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.23754},
}

RIS

TY  - UNPB
TI  - Effects of Spanwise Curvature on Hypersonic Boundary Layer Transition in Görtler-driven Flows
AU  - Andrew Welter
AU  - Ngoc Cuong Nguyen
AU  - Nicholas Webber
AU  - Mark Gragston
AU  - Jaime Peraire
AU  - Wesley Harris
PY  - 2026
DA  - 2026/10/16
PB  - arXiv
DO  - 10.48550/arxiv.2610.23754
UR  - https://arxiv.org/abs/2610.23754
AB  - The influence of spanwise convex curvature on hypersonic boundary-layer transition over a streamwise-concave surface is investigated using direct numerical simulation and Mach 7 experiments. Smooth doubly curved geometries with fixed streamwise concavity and increasing spanwise convex curvature isolate the effects of three-dimensional wall curvature on a centrifugally unstable boundary layer. Increasing spanwise curvature delays transition while preserving a Gortler-dominated route to breakdown. As spanwise curvature increases, the boundary layer thins, reducing the effective Görtler number and weakening centrifugal amplification of streamwise vortices. Consequently, growth of the primary Görtler instability is reduced, vortical structures remain closer to the wall, and secondary instability and turbulent breakdown shift downstream. Spectral proper orthogonal decomposition confirms that low-frequency vortical dynamics remain dominant in controlling transition, with sinuous secondary instability of Görtler vortices providing the principal route to breakdown. Meanwhile, boundary-layer thinning modifies acoustic instability dynamics: the second Mack mode shifts to higher frequencies and higher-frequency supersonic disturbances become increasingly prominent near breakdown as spanwise curvature increases. These acoustic disturbances remain subdominant and do not replace the Görtler-sinuous mechanism as the primary transition pathway. Numerical and experimental results exhibit consistent trends in transition location, thermal-streak organisation and disturbance evolution, supporting a common physical interpretation. These findings demonstrate that spanwise convex curvature stabilises hypersonic Görtler-dominated boundary layers, primarily by suppressing centrifugal amplification and delaying secondary instability, while leaving the transition pathway qualitatively unchanged.
ER  -

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