Scale-resolved competition between vortex stretching and viscous dissipation in three-dimensional Navier--Stokes flow

Pseudo-spectral DNS code for the paper submitted to the Journal of Fluid Mechanics: "Scale-resolved competition between vortex stretching and viscous dissipation in three-dimensional Navier–Stokes flow" Overview This repository provides a fully dealiased pseudo-spectral Navier–Stokes solver (JAX/GPU) together with all simulation scripts and figure-generation code used in the paper. The central diagnostic is the exact enstrophy budget dΩ/dt = P − D analysed through the global stretching-to-dissipation ratio R(t) = P(t)/D(t) and its shell-resolved counterpart R(k,t). Structure solver/ core.py ← NS solver engine (RK4, projection, dealiasing) diagnostics.py ← Global (Ω,P,D,R) + shell-resolved R(k,t) initial_conditions.py ← Taylor-Green, perturbed TG, ABC/Beltrami runs/ run_baseline.py → Fig.1 data (baseline TG, N=128, ν=0.01) run_viscosity.py → Fig.2 data (ν = 0.02, 0.01, 0.005) run_shell_baseline.py → Fig.3 data (shell-resolved R(k,t)) run_shell_lowvis.py → Fig.4 data (ν=0.005, T=6, shell-resolved) run_matched_energy.py → Fig.5 data (pure TG vs perturbed TG, E₀=0.5) run_abc.py → Fig.6 data (TG vs ABC/Beltrami) run_highre_safe.sh → High-Re validation (N=256, overnight runs) run_highre_single.py → Single high-Re run (called by safe.sh) figures/ generate_all_figures.py ← All 6 JFM figures (vector PDF) generate_movie.py ← Supplementary Movie 1 (R(k,t) animation) data/ ← .npz output (created by runs) run_all.sh ← One-shot execution script Quick start (Google Colab + GPU) # 1. Clone !git clone https://github.com/miosync-masa/Scale-resolved-competition.git %cd Scale-resolved-competition # 2. Install JAX with GPU !pip install jax[cuda12] # 3. Run all paper figures !bash run_all.sh # 4. Generate figures !python figures/generate_all_figures.py Requirements JAX (with GPU for speed; H100/A100 recommended) NumPy Matplotlib Summary of results Paper runs (N=128) ν Re R_max t(R_max) Ω_max t(Ω_max) R(T) Ω(T) 0.020 ~100 2.78 0.69 2.59 2.44 0.62 1.74 0.010 ~200 5.67 0.68 5.11 2.99 0.71 2.82 0.005 ~400 11.46 0.67 8.74 3.32 0.63 4.91 High-Reynolds-number validation (N=256, post-submission) Additional runs at higher Reynolds number were performed after submission to verify that the dissipative-dominance scenario persists at higher Re. These runs use N=256 grid resolution with shell-resolved diagnostics. ν Re R_max t(R_max) Ω_max R(6.0) Outcome 0.002 ~1000 28.80 0.60 24.09 0.77 Dissipation wins 0.001 ~2000 57.71 0.60 53.05 0.84 Dissipation wins Key observations from the high-Re runs: R_max scales strongly with decreasing ν — the peak stretching-to-dissipation ratio reaches 57.7 at Re~2000 — yet the global ratio still falls below unity by t=6.0 in all cases. Brief re-intensification at ν=0.001 — at t≈5.1, R briefly returns above unity (R=1.0096) before falling back, consistent with the intermittent crossover behaviour observed at ν=0.005 in the paper. No persistent production corridor is formed. The k⁴ dissipative barrier remains intact — despite the dramatically larger peak ratios, the qualitative scenario (advance → saturation → recession of the stretching-dominated spectral band) is preserved at Re~2000. These results support the paper's central conclusion: vortex stretching can be intense and spectrally mobile, but its dominance is transient, and the enstrophy budget eventually becomes controlled by viscous dissipation. To reproduce: !bash runs/run_highre_safe.sh Figure mapping Figure Script Description Fig.1 run_baseline.py Baseline TG global budget (Ω, P, D, R) Fig.2 run_viscosity.py Viscosity dependence (ν sweep) Fig.3 run_shell_baseline.py Shell-resolved R(k,t) heatmap Fig.4 run_shell_lowvis.py Low-ν long-time R(k,t) + cascade front Fig.5 run_matched_energy.py Dissipation pre-payment effect Fig.6 run_abc.py Geometry effect: TG vs ABC Movie 1 generate_movie.py R(k,t) time evolution animation