Decaying Turbulence via DNS
The asymptotic state of decaying homogeneous turbulence, resolved with record-duration direct numerical simulations.
My PhD research investigates the long-time evolution of decaying homogeneous turbulence — a fundamental open problem in fluid dynamics.
Using massively parallel pseudo-spectral Direct Numerical Simulations (up to \(4096^3\) grids) run over roughly 200,000 initial eddy-turnover times at \(Re_\lambda = 30\text{–}145\), I resolve the asymptotic decay exponent by cleanly separating the Birkhoff–Saffman (\(E(k)\sim k^2\)) and Loitsianskii–Kolmogorov–Batchelor (\(E(k)\sim k^4\)) initial-spectrum regimes. These results provide empirical benchmarks for Migdal’s recent field-theoretic predictions for decaying turbulence.
Highlights:
- Designed a dynamic regridding scheme (coarsening the grid as scales grow) that cut computational cost by more than \(5\times\) while preserving turbulence statistics.
- Built a modular single-GPU pseudo-spectral Navier–Stokes solver in C++/CUDA (cuFFT, RK2, divergence-free projection), now being extended to a multi-node multi-GPU solver with cuFFTMp/NVSHMEM and validated to machine precision.
- Developing machine-learning surrogates that couple energy-spectrum forecasting with conditional velocity-field generation, validated against DNS.
- Ran production campaigns on TACC (via ACCESS), NYU Greene, and KAUST Shaheen III, with reproducibility data and figure scripts released publicly.