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Mechanisms of transonic buffet over supercritical airfoils revealed by direct numerical simulations

This study utilizes direct numerical simulations to reveal that transonic buffet over supercritical airfoils is driven by a unified aeroacoustic feedback mechanism, where a global instability emerges from the interaction between shock motion and acoustic waves traveling along specific paths from the wake to the shock front.

Original authors: Giulio Soldati, Hang Song, Sergio Pirozzoli, Sanjiva K. Lele

Published 2026-09-24✓ Author reviewed ⓘ

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CC BY 4.0

Original authors: Giulio Soldati, Hang Song, Sergio Pirozzoli, Sanjiva K. Lele

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the high-altitude cruise of modern commercial aircraft, the air flowing over the wings moves at speeds that are a mix of the very fast and the very slow. When a plane flies at a typical cruising speed, the air accelerates over the curved top of the wing, becoming faster than sound in a small pocket before slowing down abruptly. This sudden slowdown creates a shock wave, a thin boundary where the air pressure jumps up instantly. Under normal conditions, this shock wave sits quietly in place. However, if the pilot pulls the nose of the plane up slightly to gain altitude, the shock wave can become unstable. It begins to oscillate back and forth, slamming against the wing surface with a rhythmic, low-frequency thumping. This phenomenon, known as transonic buffet, is more than just a nuisance; it causes violent shaking that can fatigue the metal structure of the aircraft, leading to cracks and potential failure. For decades, engineers have struggled to predict exactly when this shaking will start and what physical mechanism drives it, forcing them to design planes with conservative safety limits that restrict how high and fast they can fly.

To solve this mystery, a team of researchers turned to the most powerful tool available for studying fluid motion: direct numerical simulation. Instead of building a physical model in a wind tunnel, they created a perfect, virtual representation of the airflow over a supercritical airfoil—a wing shape specifically designed to delay the onset of these shock waves. Using a supercomputer, they solved the fundamental equations of motion for the air, tracking every tiny swirl and eddy of turbulence without simplifying the physics. They ran these simulations at two different scales of air density and speed, corresponding to Reynolds numbers of 300,000 and 600,000, and gradually increased the angle at which the wing met the wind. By doing so, they watched the flow transition from a smooth, stable state into the chaotic, self-sustaining shaking of full buffet.

The simulations revealed a clear sequence of events that leads to the instability. As the angle of the wing increased, the shock wave moved backward along the wing surface. At a critical point, the shock wave suddenly reversed direction, starting to move forward again. This reversal was the first sign that the flow was becoming unstable. As the angle increased further, the shock wave began to oscillate wildly. The researchers found that this shaking is not random; it is driven by a single, dominant rhythm that emerges even before the shaking becomes severe. This rhythm is a global instability, meaning the entire flow field participates in the oscillation, growing stronger until it settles into a steady, repeating cycle.

A key discovery was understanding how the air "talks" to itself to sustain this shaking. The researchers identified a feedback loop, a cycle where a disturbance travels from one part of the flow to another and returns to amplify the original motion. The cycle begins when the shock wave moves upstream, pushing the air away from the wing and creating a large pocket of separated, swirling air behind it. This turbulent pocket, located just behind the trailing edge of the wing, acts as a source of sound waves. These waves travel upstream, moving against the flow, and strike the shock wave from the front. The impact of these waves pushes the shock wave further upstream, which in turn creates more turbulence, generating more sound waves, and closing the loop.

The study provided a detailed map of how these sound waves travel. Contrary to some earlier theories that suggested the waves travel along the bottom of the wing or around the leading edge, the simulations showed that the most effective path for the sound to reach the shock wave is by traveling through the supersonic pocket of air above the wing. This path allows the sound to arrive at the shock wave from the front, which the researchers found to be the most effective way to push the shock wave and sustain the oscillation. They also found that the time it takes for the air to travel from the shock wave to the trailing edge, and for the sound to travel back, perfectly matches the period of the shaking. This confirmed that the buffet is indeed a self-sustaining cycle driven by this aeroacoustic feedback.

The researchers also investigated how the state of the air flowing over the wing before it hits the shock wave affects the shaking. They compared a lower speed case, where the air was not fully turbulent, with a higher speed case where the air was fully turbulent. They found that while the basic mechanism of the feedback loop remained the same, the speed at which the turbulence traveled downstream changed. In the lower speed case, the turbulence moved more slowly, taking longer to reach the trailing edge and generate the sound waves. This difference in travel time explained why the frequency of the shaking was slightly different between the two cases. This finding suggests that the state of the boundary layer—the thin layer of air hugging the wing—is a critical factor in determining the exact rhythm of the buffet.

By piecing together these observations, the study offers a unified picture of transonic buffet. It connects the global instability of the flow, the specific path the sound waves take, and the role of the turbulent boundary layer into a single, coherent story. The research confirms that the shaking is not caused by a single factor but by a delicate balance of forces: the shock wave's movement, the separation of the air, the generation of sound in the wake, and the return of that sound to push the shock wave again. This understanding provides a solid foundation for predicting when buffet will occur and could eventually help engineers design wings that are less prone to this dangerous shaking, allowing aircraft to fly more efficiently and safely. The work stands as a high-fidelity reference, offering a clear view of a complex physical phenomenon that has long challenged the aviation industry.

Technical Summary: Mechanisms of Transonic Buffet over Supercritical Airfoils Revealed by Direct Numerical Simulations

Problem Statement
Transonic buffet is a self-sustained, low-frequency oscillation of shock waves and boundary-layer separation on supercritical airfoils, posing significant operational hazards due to structural fatigue and aeroelastic vibrations. While the phenomenon is well-documented, the underlying physical mechanisms remain debated. Competing theories include acoustic feedback loops (Lee 1990a), where disturbances propagate upstream from the trailing edge to the shock, and global instability models (Crouch et al. 2009b), which view buffet as a Hopf bifurcation of the flow field. A critical gap exists in understanding how the incoming boundary-layer state (laminar vs. turbulent) influences the onset and dynamics of buffet, particularly given the sensitivity of Reynolds-averaged Navier–Stokes (RANS) simulations to turbulence modeling in separated flows.

Methodology
The authors present the first fully-resolved Direct Numerical Simulation (DNS) database of turbulent transonic buffet over the V2C supercritical airfoil. The study employs the in-house solver STREAmS-2.0 on the EuroHPC LUMI supercomputer.

Flow Conditions: Simulations are conducted at a freestream Mach number $M=0.7$ and chord-based Reynolds numbers of $Re = 3 \times 10^5$ and $6 \times 10^5$ . These values are selected to span distinct incoming boundary-layer states: the lower $Re$ yields a transitional boundary layer lacking a fully developed logarithmic region, while the higher $Re$ produces a fully turbulent state.
Parametric Study: The angle of attack ( $\alpha$ ) is varied from $4^\circ$ (stable) to $7^\circ$ (fully developed buffet) to capture the transition across the buffet onset threshold.
Analysis Techniques: The study utilizes Spectral Proper Orthogonal Decomposition (SPOD) to isolate coherent structures, geometrical acoustics (ray tracing) to map upstream propagation paths, and linearized shock–acoustic interaction theory to quantify shock receptivity. Space–time correlations are used to measure downstream convective times.

Key Results

Boundary-Layer Influence and Onset:
- Buffet onset is preceded by a reversal in the mean shock motion direction (moving upstream with increasing $\alpha$ ), confirming this as a necessary precursor.
- The Reynolds number dictates the separation behavior. At $Re = 3 \times 10^5$ , a shock-induced separation bubble forms at high incidence, whereas at $Re = 6 \times 10^5$ , the flow exhibits fully developed trailing-edge separation.
- Despite these differences in separation topology, the buffet Strouhal number ( $St_B$ ) remains nearly constant ( $\approx 0.09\text{--}0.11$ ) across all cases, suggesting the instability frequency is not primarily governed by the size of the separation region.
Global Instability and Modal Dynamics:
- SPOD analysis reveals a single dominant eigenmode that emerges below the buffet onset and persists into the fully developed regime.
- As $\alpha$ increases, the energy of this mode grows by approximately one order of magnitude per degree, while its spatial structure and fundamental frequency remain nearly unchanged. This behavior is consistent with a global instability saturating into a nonlinear limit cycle.
- The dominant mode exhibits an anti-phase relationship between pressure fluctuations at the shock and the near wake, linking shock motion to the periodic growth and collapse of trailing-edge separation.
Aeroacoustic Feedback Mechanism:
- Source Location: Turbulent shear stress analysis identifies the near wake (rather than the trailing edge) as the dominant acoustic source, due to massive flow separation limiting the validity of compact dipole assumptions.
- Propagation Paths: Geometrical acoustics identifies two paths connecting the near-wake source to the shock: a shorter "back-impinging" path and a longer "front-impinging" path that circumvents the shock tip.
- Shock Receptivity: Linearized shock–acoustic interaction theory demonstrates that the shock acts as a low-pass filter and is significantly more receptive (approx. 2x response) to front-impinging acoustic disturbances than to back-impinging ones.
- Feedback Loop: The establishment of a continuous downstream path for pressure disturbances is linked to the intermittent complete separation of the boundary layer. The sum of the upstream acoustic time (along the front-impinging path) and the downstream convective time aligns with the measured buffet period for both Reynolds numbers.

Significance and Claims
The paper claims to provide a unified picture of transonic buffet that reconciles previously separate perspectives:

It validates the global instability framework by showing a single mode saturating into a limit cycle.
It supports the aeroacoustic feedback model by identifying the specific physical pathways (front-impinging rays) and confirming the shock's preferential receptivity to upstream-traveling waves.
It clarifies the role of flow separation, demonstrating that the downstream leg of the feedback loop only becomes continuous when the boundary layer is fully separated, which explains the Reynolds-number dependence of the buffet period.

The authors conclude that this high-fidelity DNS database serves as a benchmark for lower-order modeling (e.g., RANS closures) and provides a controlled 2D baseline for future studies of buffet on swept wings. They modestly note that their assessment relies on approximations (e.g., applying geometrical acoustics to mean flow) and that the exact combination of paths governing the period requires further investigation via linear stability analysis.

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