The structure of a turbulent boundary layer studied by numerical simulation (1010.4000v1)

Abstract: Time-dependent visualisations of large-scale direct and large-eddy simulations (DNS and LES) of a turbulent boundary layer reaching up to $Re_\theta=4300$ are presented. The focus of the present fluid dynamics video is on analysing the coherent vortical structures in the boundary layer: It is clearly shown that hairpin vortices are indeed present in the simulation data, however they are characteristic remainders of the laminar-turbulent transition at lower Reynolds numbers. At higher $Re$ (say $Re_\theta>2000$), these structures are no longer seen as being dominant; the coherence is clearly lost, both in the near-wall region as well as in the outer layer of the boundary layer. Note, however, that large-scale streaks in the streamwise velocity, which have their peak energy at about half the boundary-layer thickness, are unambiguously observed.

• The paper demonstrates that coherent hairpin vortices emerge in transitional boundary layers at low Reynolds numbers (Reθ ≈ 800) through high-resolution DNS.
• The paper finds that at higher Reynolds numbers (Reθ > 2000), the organized hairpin structures are replaced by large-scale, unstructured vortices in fully turbulent flow.
• The paper reveals dual spectral features that highlight the interaction between near-wall streaks and outer-layer structures, emphasizing the evolving turbulence dynamics.

Analysis of Turbulent Boundary Layers via Numerical Simulation

The paper "The structure of a turbulent boundary layer studied by numerical simulation" by Schlatter et al. offers an in-depth investigation into the nature of turbulent boundary layers using advanced numerical methods such as Direct Numerical Simulation (DNS) and Large-Eddy Simulation (LES). The research is centered on the identification and analysis of coherent vortical structures, namely hairpin vortices, within turbulent boundary layers at different stages of the flow, particularly focusing on conditions with Reynolds numbers up to $Re_\theta=4300$.

Objective and Methodological Approach

The paper employs simulations on a canonical turbulent boundary layer without pressure gradient, initiated from a laminar Blasius boundary layer, which transitions to turbulence due to a deliberate random volumetric force, likened to a tripping strip in experimental setups. The domain parameters, chosen meticulously, allow the simulations to span a Reynolds number range from $Re_\theta=180$ to $Re_\theta=4300$, ensuring fully-developed turbulence from $Re_\theta \approx 500$.

The DNS encompasses a high numerical resolution grid system involving $7.5 \times 10^9$ grid points across spectral modes, while the LES model utilizes a less stringent resolution, although still sufficient to capture significant flow structures. These simulations require substantial computational power, reflecting the complexity and resource-intensive nature of turbulence studies.

Key Findings

1. Transition and Hairpin Vortices: The simulations confirm that hairpin vortices—the historically identified coherent structures in transitional boundary layers—are predominant at lower Reynolds numbers (e.g., $Re_\theta \approx 800$). The identification of such structures is facilitated through visualization of isocontours of negative $\lambda_2$ criteria.
2. High-Reynolds-Number Dynamics: As the flow transitions to higher Reynolds numbers ($Re_\theta > 2000$), the prominence of coherent hairpin vortices diminishes. At $Re_\theta=4300$, the vortical structures observed are significantly large-scale and unstructured compared to their low-Re counterparts, indicating a complete loss of dominance by the hairpin structures in a fully turbulent boundary layer.
3. Spectral Characteristics: The paper highlights two key spectral features within the boundary layer: turbulent streaks in proximity to the wall associated with inner viscosity units, and extensive structures scaling with outer units. This dual-scale observation suggests an ongoing interaction between these inner and outer layer structures that varies with Reynolds number.

Implications for Future Research

The implications of these findings suggest a nuanced understanding of boundary layer turbulence as a function of Reynolds number, emphasizing the transitional phase's uniqueness in structure formation, contrasted against a more chaotic large-scale structuring at higher $Re_\theta$. This research underscores the evolutionary nature of coherent structures within boundary layers and their diminishing organized presence at elevated Reynolds numbers.

Future investigations could explore the specific mechanisms driving the modulation of near-wall streaks by outer-layer structures, particularly at these higher Reynolds numbers. Exploring different inflow conditions or geometries might offer additional insights into the scalability of the identified phenomena, further bridging gaps between numerical simulations and practical applications in engineering and geophysical processes.