Fisher Information Dynamics of Three-Dimensional Turbulent Velocity Fields: Diagnostic Analysis of Gradient Sharpening

This dataset contains numerical results and analysis code for Fisher information dynamics of three-dimensional turbulent velocity fields. The analysis uses direct numerical simulation (DNS) data from the Johns Hopkins Turbulence Database (JHTDB) to study gradient sharpening in turbulence. KEY FINDINGS: The Fisher information (gradient sharpness) of velocity magnitude is decomposed using the five-term decomposition. For incompressible periodic flow, only shear production and diffusion dissipation contribute: - Shear Production (T₂): +129.82 Dominant mechanism for gradient production. Contains all 3D strain rate effects, including vortex tube stretching. This is the correct physical interpretation following rigorous mathematical derivation. - Diffusion Dissipation (T_diff): -85.87 Molecular diffusion with D = 1.85 × 10⁻⁴. No artificial tuning employed. - Net Production: +43.95 Positive value indicates non-equilibrium state with active gradient sharpening. Corresponds to energy cascade origin at large scales. Fisher Information: C = 115.88Indicates strong gradient localization in filamentary structures. IMPORTANT NOTES: ✓ Uses CORRECT five-term decomposition (not six-term)✓ Shear term T₂ contains ALL 3D effects including vortex stretching✓ No artificial balancing or tuning of diffusion coefficient✓ Results are from representative time snapshot t=420 DATA FILES: 1. fisher_3d_analysis_corrected.py Complete analysis code that reads HDF5 data and computes all quantities. 2. C_3d.npy - Fisher information value (115.88) 3. T2_3d.npy - Shear production term (+129.82) 4. Tdiff_3d.npy - Diffusion dissipation term (-85.87) 5. figure1_3d_velocity.png - 3D velocity field structure 6. figure2_3d_fisher.png - Fisher information spatial distribution 7. figure3_decomposition_corrected.png - Five-term decomposition results 8. figure4_interpretation_corrected.png - Physical interpretation DATA SOURCE: - Database: Johns Hopkins Turbulence Database (JHTDB)- Dataset: isotropic1024coarse- Spatial Resolution: 1024³ grid points- Temporal Snapshot: t = 420 (large-eddy turnover time)- File Size: 8.59 GB- Variables: Velocity components (u, v, w) and pressure METHODOLOGY: 1. Data Loading: Read HDF5 file, downsample from 1024³ to 512³2. Scalar Field: Use velocity magnitude |u|, normalize ρ = |u|/⟨|u|⟩3. Fisher Information: C = ∫ρ|∇lnρ|²dx4. Decomposition: - Shear term: T₂ = -2∫ρ S:(∇lnρ ⊗ ∇lnρ)dx - Diffusion: T_diff = -2D∫ρ|∇∇lnρ|²dx - D = 1.85 × 10⁻⁴ (molecular) This analysis corrects earlier work that incorrectly separated vortex stretching as an independent term. The correct five-term decomposition shows that vortex stretching effects are contained within the shear term T₂. For dual-field comparison with vorticity magnitude, see related work. CITATION: If you use this dataset, please cite:[DOI will be assigned by Zenodo] And the associated paper (when published):Wu, Y. (2026). Fisher Information Dynamics of Three-Dimensional Turbulent Velocity Fields: Non-Equilibrium Gradient Sharpening. Physics of Fluids. LICENSE: CC BY 4.0 CONTACT:Yingchuan WuInstitute of Aerospace TechnologyChina Aerodynamics Research and Development CenterEmail: [e-mail]