Lukas M. Fuchs | Searcharxiv

arXiv2026

Spectral analysis of attached and separated turbulent flows over a Gaussian-shaped bump

We investigate the broadband turbulent dynamics of attached and separated flows over a Gaussian bump, focusing on the origin of low-frequency coherent structures. The analysis combines time-resolved experimental measurements with physics-based linear models, using mean fields previously assimilated from the same dataset as base flows. Spectral proper orthogonal decomposition reveals coherent dynamics in low- and medium-frequency regimes for both flows, with the low-frequency dynamics being substantially stronger in the separated case. In the separated flow, these dynamics are linked to a three-dimensional zero-frequency modal instability that generates large-scale streamwise-elongated structures downstream of the bump. A standing-wave model based on resolvent modes, incorporating finite-span effects, reproduces the experimentally observed spanwise structure of the dynamics and highlights the limitations of simulations with small spanwise extent and periodic boundary conditions. In the attached flow, similar low-frequency structures are identified. These are weaker, do not form a prominent standing-wave pattern, and cannot be definitively classified as either modal or non-modal. The three-dimensional zero-frequency instability and finite-span standing-wave dynamics are identified as the main drivers of low-frequency coherent structures in the separated flow. They offer an explanation for persistent discrepancies between simulations and experiments on the Gaussian bump, and provide guidance on spanwise domain size and boundary conditions for future simulations.

physics.flu-dyn↗

arXiv2026

Standing-Wave Dynamics in Low-Frequency Breathing of a Turbulent Separation Bubble

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.

physics.flu-dyn↗