Classically studied coherent structures only paint a partial picture of wall-bounded turbulence
Unlocking the Unseen: AI-Driven Insights into Turbulent Flows
This paper presents a data-driven methodology to identify high-importance regions in wall-bounded turbulent flows, which differ from classical coherent structures. Using deep learning and explainability algorithms, the study aims to objectively identify regions crucial for flow evolution, offering new insights into turbulence mechanisms.
Executive Summary: Unveiling New Turbulence Dynamics
The Challenge with Classical Turbulence Models
For over 140 years, the complex mechanisms of energy transport and dissipation in turbulent flows have remained largely elusive. Traditional approaches have focused on 'coherent structures'—organized flow patterns defined by spatial coherence and contribution to momentum/energy transfer. However, their precise connection to overall flow development is still unclear, leading to an incomplete understanding.
Introducing Data-Driven Importance Identification
This research pioneers a data-driven methodology to objectively identify 'high-importance regions' in turbulent flows. By training a deep-learning model to predict future flow states and using the gradient-SHAP explainability algorithm, the study calculates the 'importance' of each grid point. This allows for the computation of high-importance regions, which are then rigorously compared to classically defined coherent structures.
Key Findings: Beyond Traditional Structures
The SHAP analysis reveals regions of high importance that show varying levels of agreement with classical structures (like Reynolds-stress events, streaks, and vortices) but are not entirely reducible to any single one. This implies that classical coherent structures, while significant, only paint a partial picture. The data-driven approach uncovers complex, nonlinear patterns previously not identified, especially far from the wall. This objective identification offers a new paradigm for understanding and potentially controlling turbulence more effectively.
140+
Years of Unanswered Questions in Turbulence
15%
Global Energy Consumption due to Turbulence
90%
Agreement with Streaks (y⁺ ~ 13)
60%
Coincidence with Q-Events (SHAP Structures)
Deep Analysis & Enterprise Applications
Select a topic to dive deeper, then explore the specific findings from the research, rebuilt as interactive, enterprise-focused modules.
The Turbulence Problem
Data-Driven SHAP Methodology
SHAP Structures & Insights
Implications for Turbulence Control
The Turbulence Problem
Turbulent flows, governed by non-linear Navier-Stokes equations, exhibit multi-scale behavior making analytical solutions impossible. Direct Numerical Simulations (DNS) are computationally intensive, highlighting the need for alternative approaches to understand energy transfer and control mechanisms. Classical approaches based on 'coherent structures' like streaks, Reynolds-stress events, and vortices have provided insights but lack a unified, objective framework for assessing their overall importance.
Data-Driven SHAP Methodology
Our methodology employs a U-net deep-learning model, trained on 10,000 instantaneous flow fields, to predict future flow states. The gradient-SHAP algorithm then quantifies the importance of each grid point in these predictions. By calculating the mean-squared error (MSE) of predictions, SHAP values identify the most influential regions for velocity fluctuation evolution over a viscous time Δt⁺ = 5. This method offers an objective measure of causal importance.
SHAP Structures & Insights
The SHAP analysis reveals 'high-importance regions' that are not perfectly aligned with any single classical structure. While strong correlations exist (e.g., with sweeps near the wall, and streaks around y⁺ ≈ 15), SHAP structures also identify unique, complex, nonlinear patterns. This suggests classical structures only offer a partial view. Notably, the SHAP structures provide a global, objective assessment of regions critical for flow evolution, paving the way for more efficient turbulence control strategies.
Implications for Turbulence Control
This research provides a new paradigm for analyzing physical problems by objectively identifying causally important regions. The SHAP framework can be applied to other flow cases (e.g., wall-mounted obstacles) and various fields (thermal, cavitation). It offers a scalable methodology that directly relates to wall-normal distance, facilitating the development of more efficient turbulence control strategies by targeting these objectively identified high-importance regions. Future work includes exploring longer prediction horizons and different output variables.
40-50%
of SHAP Structures Uncorrelated with Reynolds Stress – Uncovering Novel Dynamics
Enterprise Process Flow
U-Net Model Training
→
Gradient-SHAP Calculation
→
High-Importance Region Segmentation
→
Comparison with Classical Structures
| Feature | Classical Coherent Structures | SHAP-based Structures (This Study) |
|---|---|---|
| Definition Basis | Defined by specific physical effects (e.g., vorticity, Reynolds stress events, velocity gradients) | Objectively identified by causal importance for future flow prediction using XAI (SHAP values) |
| Scope of Importance | Focus on specific types of energy/momentum transfer or rotation; partial picture | Global assessment across all flow regions, identifying most influential points for overall flow evolution |
| Novelty | Established, well-documented patterns (streaks, Q-events, vortices) | Uncovers complex, nonlinear patterns not fully captured by classical definitions, especially at higher Re or away from the wall |
| Application | Understanding specific turbulence phenomena | Directly supports development of more efficient, targeted turbulence control strategies |
Impact Beyond Channels: Wall-Mounted Obstacles
The SHAP framework has already demonstrated its versatility in other complex flow cases. For instance, in flows around a wall-mounted square obstacle, SHAP values highlight the critical influence of the wall and the obstacle itself. This approach significantly reduces the perceived importance of streaks compared to traditional analyses, while demonstrating similar importance for Q events and a lower importance for vortices. This ability to adapt and provide objective insights across different flow geometries underscores its potential for broad application in industrial fluid dynamics problems.
Calculate Your Potential AI-Driven Efficiency Gains
Estimate the impact of objective, AI-driven turbulence analysis on your operational efficiency and cost savings. Fine-tune the parameters to see your enterprise's potential ROI.
Estimated Annual Savings
$0
Reclaimed Productive Hours Annually
0
Your Roadmap to Advanced Turbulence Insights
Our structured implementation ensures a seamless integration of SHAP-based analysis into your fluid dynamics research and control strategies.
Phase 1: Data Acquisition & Model Training
Securely gather existing DNS data or prepare for new simulations. Train and validate the U-net deep learning model to accurately predict future flow states based on your specific turbulent flow conditions.
Phase 2: SHAP Value Calculation & Structure Identification
Apply the Gradient-SHAP algorithm to the trained model to compute importance scores for every grid point. Utilize percolation analysis to segment and identify the 'SHAP structures' – the objectively defined high-importance regions in your flow.
Phase 3: Comparative Analysis & Strategic Insights
Statistically compare the newly identified SHAP structures with classical coherent structures (streaks, Q-events, vortices). Generate actionable insights that highlight unique, high-impact regions for targeted turbulence control and optimization strategies.
Phase 4: Integration & Ongoing Optimization
Integrate SHAP-derived insights into your existing computational fluid dynamics (CFD) workflows or experimental design. Establish continuous feedback loops to refine models and strategies, ensuring sustained performance improvements and innovative control solutions.
Ready to Redefine Your Turbulence Analysis?
Stop relying on partial pictures. Discover how objective, AI-driven insights can revolutionize your understanding and control of turbulent flows. Our experts are ready to guide you.
Ready to Get Started?
Book Your Free Consultation.
Let's Discuss Your AI Strategy!
Lets Discuss Your Needs
Select a Date
Sun
Mon
Tue
Wed
Thu
Fri
Sat