This paper presents a computational study identifying dominant flow structures, their frequencies, and the correla tions with the wall pressure signal in a turbulent backward facing step. A long-term goal of this study is to identify po tential strategies for a design of metamaterials to control flow separation in turbulent flows. We perform Direct Numerical Simulations (DNS) of flow over a backward-facing step at Reh =5100with a spectral-element method. To provide a turbulent inflow to the step, we perform simultaneous auxiliary simula tions of a turbulent half-channel flow that intersects with the step domain. We apply spectral analysis to extract dominant spatial and temporal patterns from the flow. We focus on key regions: upstream, near-wake, far-wake, and the recirculation bubble to understand how different flow features, such as shear layer flapping and vortex shedding, are reflected in wall sig nals. Two main questions guide our work: 1) What are the dominant frequencies driving the separated flow? 2) Where should metamaterial strips be placed to interact with these dy namics? Our results show distinct frequency peaks, with a low-frequency component at St ≈ 0.003, associated with large scale recirculation bubble oscillations, and higher-frequency content around St ≈ 0.02, corresponding to shear-layer flap ping dynamics. To further characterize these dynamics, we apply Proper Orthogonal Decomposition (POD) to the pres sure field, where the leading modes capture dominant low frequency behavior consistent with the bubble oscillations ob served in the spectra, reinforcing the link between pressure sig nals and coherent flow structures. These findings suggest that the upstream region and the area beneath the recirculation bub ble are promising locations for control, as they exhibit strong, coherent signatures in the pressure field. The identified low and intermediate-frequency bands (St ≈ 0.003 and St ≈ 0.02) provide relevant targets for the design of metamaterial-based f low control strategies.

Improving turbulent flow control is crucial for various applications like reducing drag, enhancing mixing, and managing heat transfer. Feedback control approaches, which sense the turbulent signal in the flow and modify the actuation depending on the value of the signal, such as opposition control or a wall-sensing control, have proven to be effective. However, these approaches use the full, unfiltered signal, which naturally contains multiple frequencies. In conjunction with a recent interest in passive frequency-tuned surfaces that selectively respond to a single frequency or a band of frequencies, this paper explores a feedback-control approach that focuses on specific frequencies. We compare the frequency-tuned approach with the classical opposition control (that senses flow velocity in some off-wall location) and with our previously-developed wall-sensing control (that acts upon a wall shear stress), both using unfiltered temporal signals (across all frequencies). Initial findings show a drag reduction of 21.11% at Re_tau ≈ 180 and 18% atRe_tau ≈ 390 using classical opposition control, and 10.64% at Re_tau ≈ 180 and 7.12% at Re_tau ≈ 390 using wall-sensing control, demonstrating some reduction in effectiveness for wall-sensing strategy. The frequency-tuned method developed in this study achieved only modest drag reductions, ranging between 1% and 2% for Re_tau ≈ 180, and even showed a slight drag increase of 1% to 2% with higher Reynolds numbers (Re_tau ≈ 390). This outcome highlights the limitations of relying on a single-frequency control strategy, which proves inadequate for managing complex turbulence dynamics that has a broadband spectrum, especially at higher Reynolds numbers.

Turbulent flow control plays a pivotal role in diverse applications such as drag reduction, mixing, heat transfer, and boundary layer and flow separation control. Although numerous active and passive methods have been explored for mitigating drag in turbulent flows, this study introduces an approach, not widely explored, that utilizes wall-sensing based on wall shear stress. We conduct a comparative analysis with the opposition control method, which uses velocity sensing at an off-wall location. The results from opposition control reveal significant drag reduction: 21.11% at Re_tau ≈ 180 and 18% at Re_tau ≈ 390. In contrast, the wall-sensing method achieves drag reductions of 10.64% at Re_tau ≈ 180 and 7.12% at Re_tau ≈ 390. This relative ineffectiveness of the wall-sensing control method is attributed to a high-frequency content of the wall shear stress data, which, if undamped, may lead to oscillations in the applied control signal. This, in turn, requires either a reduction in gain, or ‘freezing’ of the control input in time to arrive at a stable control implementation, reducing the method effectiveness as compared to an opposition control approach.