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

TL;DR

This study combines experimental and modeling approaches to analyze low-frequency turbulent structures over a Gaussian bump, revealing the role of three-dimensional instabilities and finite-span effects in separated flows.

Contribution

It introduces a physics-based linear model incorporating finite-span effects to explain low-frequency turbulence dynamics over a Gaussian bump, highlighting the importance of spanwise domain considerations.

Findings

Separated flow exhibits stronger low-frequency dynamics than attached flow.

A zero-frequency modal instability drives large-scale structures in separated flow.

Finite-span effects are crucial for accurately reproducing observed turbulent structures.

Abstract

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.