Standing-Wave Dynamics in Low-Frequency Breathing of a Turbulent Separation Bubble
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2025
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| author | Fuchs, Lukas M. Steinfurth, Ben von Saldern, Jakob G. R. Weiss, Julien Oberleithner, Kilian |
| author_facet | Fuchs, Lukas M. Steinfurth, Ben von Saldern, Jakob G. R. Weiss, Julien Oberleithner, Kilian |
| contents | This study investigates the low-frequency dynamics of a turbulent separation bubble (TSB) over a backward-facing ramp, with a focus on large-scale coherent structures associated with the so-called 'breathing motion'. Using time-resolved particle image velocimetry (PIV) in both streamwise and spanwise planes, we examine the role of sidewall confinement. Spectral proper orthogonal decomposition (SPOD) of the streamwise velocity field reveals a dominant low-rank mode at low Strouhal numbers ($St < 0.05$), consistent with prior observations of TSB breathing. Strikingly, the spanwise-oriented PIV data uncover a previously unreported standing wave pattern, characterised by discrete spanwise wavenumbers and nodal/antinodal structures, suggesting the presence of spanwise resonance. To explain these observations, we construct a resolvent-based model that imposes free-slip conditions at the sidewall locations by superposing left- and right-traveling three-dimensional modes. The model accurately reproduces the measured SPOD modes, demonstrating that sidewall reflections lead to the formation of standing wave-like patterns. To gain further insight into the driving mechanisms of the low-frequency dynamics, a global stability analysis is performed, revealing a zero-frequency eigenmode whose growth rate depends on the spanwise wavenumber. This eigenmode originates from a centrifugal instability. Downstream, the associated coherent structures are further amplified through non-modal lift-up mechanisms. Our findings highlight the critical influence of spanwise boundary conditions on the selection and structure of low-frequency modes in TSBs. This has direct implications for both experimental and numerical studies, particularly those relying on spanwise-periodic boundary conditions, and offers a low-order framework for predicting sidewall-induced modal dynamics in separated flows. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_24723 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Standing-Wave Dynamics in Low-Frequency Breathing of a Turbulent Separation Bubble Fuchs, Lukas M. Steinfurth, Ben von Saldern, Jakob G. R. Weiss, Julien Oberleithner, Kilian Fluid Dynamics This study investigates the low-frequency dynamics of a turbulent separation bubble (TSB) over a backward-facing ramp, with a focus on large-scale coherent structures associated with the so-called 'breathing motion'. Using time-resolved particle image velocimetry (PIV) in both streamwise and spanwise planes, we examine the role of sidewall confinement. Spectral proper orthogonal decomposition (SPOD) of the streamwise velocity field reveals a dominant low-rank mode at low Strouhal numbers ($St < 0.05$), consistent with prior observations of TSB breathing. Strikingly, the spanwise-oriented PIV data uncover a previously unreported standing wave pattern, characterised by discrete spanwise wavenumbers and nodal/antinodal structures, suggesting the presence of spanwise resonance. To explain these observations, we construct a resolvent-based model that imposes free-slip conditions at the sidewall locations by superposing left- and right-traveling three-dimensional modes. The model accurately reproduces the measured SPOD modes, demonstrating that sidewall reflections lead to the formation of standing wave-like patterns. To gain further insight into the driving mechanisms of the low-frequency dynamics, a global stability analysis is performed, revealing a zero-frequency eigenmode whose growth rate depends on the spanwise wavenumber. This eigenmode originates from a centrifugal instability. Downstream, the associated coherent structures are further amplified through non-modal lift-up mechanisms. Our findings highlight the critical influence of spanwise boundary conditions on the selection and structure of low-frequency modes in TSBs. This has direct implications for both experimental and numerical studies, particularly those relying on spanwise-periodic boundary conditions, and offers a low-order framework for predicting sidewall-induced modal dynamics in separated flows. |
| title | Standing-Wave Dynamics in Low-Frequency Breathing of a Turbulent Separation Bubble |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2505.24723 |