RG_NS_SLB_15

Description

Python code: 1. Kolmogorov_turbulence_&_RG_effective_viscosity.py 2. Hydrodynamic_Stability_&_Inertial_Range_Diagnostics.py

Steps to reproduce

text = """ 1. Methods & Protocols The dataset was generated using a high-resolution, pseudo-spectral solver integrating the 3D Stochastic Navier-Stokes equations under an asymptotically safe, field-theoretic renormalization group (RG) forcing scheme. Grid: Periodic, isotropic $256^3$ nodes with Orszag 2/3-truncation rule dealiasing ($k_{max} \approx 85$). Time integration: Third-order, semi-implicit Runge-Kutta (RK3) scheme for stability. Convergence: Continuous large-scale forcing ($1 \le k \le 2.5$) until steady state. Data accumulated over $60$ eddy turnover times ($t/\tau_f$) to verify fixed-point stability. 2. Software & Infrastructure Platform: Executed in a Linux container environment on Google Kaggle (User ID: innshrestha). Hardware: Intel Xeon CPU paired with a Tesla P100 GPU to accelerate 3D Fast Fourier Transforms (FFTs). Software Ecosystem: Compiled and run using Python 3.12. Libraries: `numpy` (v1.26.4) for tensor arrays, `scipy` (v1.12.0) for GPU-parallelized 3D FFTs, and `matplotlib` (v3.8.3) for computing logarithmic slopes and compiling figures. 3. Step-by-Step Workflow 1. Environment Setup: Install dependencies: `pip install numpy scipy matplotlib` 2. Solver Execution: Run `stochastic_navier_stokes_256.py` to initialize velocity fields, execute the stochastic forcing loop, and save Fourier coefficients as compressed `.npy` files. 3. Data Extraction (Fig 1): The script logs the spatial supremum of vorticity at each time step and evaluates $\int_0^t \Vert{}\omega\Vert{}_{L^\infty} ds$ to output the bounded Beale-Kato-Majda (BKM) integral trace. 4. Spectral Analysis (Fig 2): The solver computes the shell-averaged kinetic energy spectrum $E(k)$. A central-difference gradient operator calculates the local scaling exponent $\alpha = d\ln E(k)/d\ln k$. 5. Plotting: Run `plot_diagnostics.py` to plot the profiles and shade boundaries across the unpolluted inertial zone ($10 \le k \le 50$) and the bottleneck contamination region ($50 \le k \le 80$)."""

Institutions

• Kaggle

  California, San Francisco

Categories

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