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Characterisation of the secondary instability in a 1 : 3 sudden expansion through inviscid structural sensitivity.

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Title: Characterisation of the secondary instability in a 1 : 3 sudden expansion through inviscid structural sensitivity.
Authors: Santoriello, Roberta1 (AUTHOR), Giannetti, Flavio1,2 (AUTHOR) fgiannetti@unisa.it, Auteri, Franco1,2 (AUTHOR), Citro, Vincenzo1,2 (AUTHOR)
Source: Journal of Fluid Mechanics. 11/25/2025, Vol. 1023, p1-24. 24p.
Subjects: Flow instability, Inviscid flow, Bifurcation theory, Stability criterion, Stability theory, Hypothesis, Reynolds number
Abstract: The inviscid mechanism, driving flow instabilities in a $1:3$ , planar and symmetric sudden expansion, is discerned through a sensitivity-based protocol, also referred to as inviscid structural sensitivity analysis, with a specific focus on the onset and nature of the secondary instability. The fundamental idea of this methodology is to change the contribution of viscosity solely in the global stability equations, while freezing the base-flow field at the critical conditions. This is practically implemented by decoupling the Reynolds number that serves as the control parameter for determining the steady base flow from that governing the disturbance evolution, in order to repeat the structural sensitivity analysis while progressively increasing the Reynolds number in the linearised equations only. Accordingly, the sequence of structural sensitivity maps enables us to highlight the flow regions where the inviscid instability mechanism acts. The numerical results reveal that the classical structural sensitivity analysis accurately locates the wavemaker region within the primary recirculation zone, but only its inviscid limit can unveil that the core of the instability coincides with the centre of the primary vortex: a hallmark of an elliptic instability. To validate the global findings, the results of the inviscid structural sensitivity analysis are compared with those obtained from geometric optics. The agreement of the two approaches confirms the inviscid character of the instability, thereby providing a complete picture of the nature of the secondary bifurcation. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Fluid Mechanics is the property of Cambridge University Press and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Characterisation of the secondary instability in a 1 : 3 sudden expansion through inviscid structural sensitivity.
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Fluid+Mechanics%22">Journal of Fluid Mechanics</searchLink>. 11/25/2025, Vol. 1023, p1-24. 24p.
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  Data: <searchLink fieldCode="DE" term="%22Flow+instability%22">Flow instability</searchLink><br /><searchLink fieldCode="DE" term="%22Inviscid+flow%22">Inviscid flow</searchLink><br /><searchLink fieldCode="DE" term="%22Bifurcation+theory%22">Bifurcation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Stability+criterion%22">Stability criterion</searchLink><br /><searchLink fieldCode="DE" term="%22Stability+theory%22">Stability theory</searchLink><br /><searchLink fieldCode="DE" term="%22Hypothesis%22">Hypothesis</searchLink><br /><searchLink fieldCode="DE" term="%22Reynolds+number%22">Reynolds number</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: The inviscid mechanism, driving flow instabilities in a $1:3$ , planar and symmetric sudden expansion, is discerned through a sensitivity-based protocol, also referred to as inviscid structural sensitivity analysis, with a specific focus on the onset and nature of the secondary instability. The fundamental idea of this methodology is to change the contribution of viscosity solely in the global stability equations, while freezing the base-flow field at the critical conditions. This is practically implemented by decoupling the Reynolds number that serves as the control parameter for determining the steady base flow from that governing the disturbance evolution, in order to repeat the structural sensitivity analysis while progressively increasing the Reynolds number in the linearised equations only. Accordingly, the sequence of structural sensitivity maps enables us to highlight the flow regions where the inviscid instability mechanism acts. The numerical results reveal that the classical structural sensitivity analysis accurately locates the wavemaker region within the primary recirculation zone, but only its inviscid limit can unveil that the core of the instability coincides with the centre of the primary vortex: a hallmark of an elliptic instability. To validate the global findings, the results of the inviscid structural sensitivity analysis are compared with those obtained from geometric optics. The agreement of the two approaches confirms the inviscid character of the instability, thereby providing a complete picture of the nature of the secondary bifurcation. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Fluid Mechanics is the property of Cambridge University Press and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1017/jfm.2025.10812
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      – Code: eng
        Text: English
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        PageCount: 24
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      – SubjectFull: Flow instability
        Type: general
      – SubjectFull: Inviscid flow
        Type: general
      – SubjectFull: Bifurcation theory
        Type: general
      – SubjectFull: Stability criterion
        Type: general
      – SubjectFull: Stability theory
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      – SubjectFull: Hypothesis
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      – SubjectFull: Reynolds number
        Type: general
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      – TitleFull: Characterisation of the secondary instability in a 1 : 3 sudden expansion through inviscid structural sensitivity.
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            NameFull: Santoriello, Roberta
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            NameFull: Giannetti, Flavio
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            NameFull: Auteri, Franco
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              Text: 11/25/2025
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              Y: 2025
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