Many exercises ask you to derive:
These are standard results. Compare your derivations to any graduate turbulence textbook, e.g.: A First Course In Turbulence Solution Manual
Compare your full solution to the manual's. Note any differences. If your answer is algebraically different but physically equivalent, prove it. This process builds deep, lasting intuition. Many exercises ask you to derive:
Spend at least two hours on a single problem. Write down your approach, even if you get stuck. Identify the exact step where you cannot proceed (e.g., "I don't know how to apply the Fourier transform to the nonlinear term"). These are standard results
Platforms like ResearchGate and Academia.edu occasionally feature PDFs labeled "Tennekes_Lumley_Solutions.pdf." However, verify the author. Many are fan-made and contain critical algebraic errors (especially in the derivation of the spectral energy transfer function). Cross-reference any answer you find from these sources.