The Old Road to Turbulence
| Discovery Year | Portrait | Key Contribution |
|---|---|---|
| 1500s |
|
Leonardo da Vinci: Documented early observations of turbulent flow. |
| 1820s |
|
Claude-Louis Navier and George Gabriel Stokes: Formulated the foundational NS equations. |
| 1883 |
|
Osborne Reynolds: Characterized the transition to turbulence. |
| 1941 |
|
Andrey Kolmogorov: Proposed scaling laws of turbulence (K41). |
| 1944 |
|
Werner Heisenberg: Theoretical contributions to stability and dissipation models. |
| 1946 |
|
Lars Onsager: Introduced insights into fractal velocity fields and vortex structures. |
| 1948-1952 |
|
Eberhard Hopf: The functional equation for statistics of turbulence. |
| 1956 |
|
Lev Landau: Advanced the understanding of hydrodynamic stability. |
| 1985 |
|
Giorgio Parisi and Uriel Frisch: Proposed multifractal models for turbulence. |
| 2000-2022 |
|
K.R. Sreenivasan: DNS studies uncovering scaling law violations. |
Scaling Law Violations: The Dead End of the Old Road
Key Findings:
- Kolmogorov's K41 model theory: Predicted universal scaling laws for velocity difference moments, including an index of \( \frac{2}{3} \) for the second moment.
- This figure shows the effective index = logarithmic derivative of the second moment \( \langle \Delta v^2(r,t) \rangle \) plotted against \( \log \left( \frac{r}{\sqrt{t}} \right) \).
- DNS simulations (\( 4096^3 \) lattice) using a novel method to extract effective indices from observed energy spectra contradicted any scaling law (a horizontal line on this plot).
