| integral scale L / velocity U | |
| dissipation rate ε ≈ U³/L | |
| Kolmogorov length η = (ν³/ε)1/4 | |
| Kolmogorov velocity uη = (νε)1/4 / time τη = (ν/ε)1/2 | |
| scale separation L/η (should equal Re3/4) | |
| DNS grid points N ≈ (L/η)³ = Re9/4 | |
| DNS memory for one velocity field (float64) |
The spectrum is the standard model form: a von Kármán roll-off at the integral scale, Kolmogorov's −5/3 inertial range, and an exponential cutoff at the dissipation scale. Slide Re and watch the inertial range widen as Re3/4 — and the grid-point count explode as Re9/4.