Science Advances

Supplementary Materials

This PDF file includes:

  • section S1. Derivation of the Euler-Lagrange equation
  • section S2. The Navier-Stokes equation
  • section S3. Newton iterations
  • section S4. Sensitivity to parameters
  • section S5. Computing the probability of extreme events
  • section S6. Supporting computational results
  • fig. S1. Evolution of the energy input versus mean flow.
  • fig. S2. Triad interactions.
  • fig. S3. Sensitivity of the optimal solutions.
  • fig. S4. Joint PDFs for higher Reynolds numbers.
  • fig. S5. Prediction of intermittent bursts at higher Reynolds numbers.
  • table S1. Simulation parameters.
  • Legend for movie S1
  • References (39–42)

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Other Supplementary Material for this manuscript includes the following:

  • movie S1 (.mp4 format). The prediction of an extreme event in the Kolmogorov flow.

Files in this Data Supplement: