THE TURBULENCE THAT MATTERS

A unified expression far the spectrum of turbulence is developed by as ymptotically matching known expressions for small and large wave numbe rs, and a formula for the one-dimensional spectral function, which dep ends on the turbulence Reynolds number Re-lambda, is provided. In addi tion, formulas relating all the length scales of turbulence are provid ed. These relations also depend an Reynolds number The effects of free -stream turbulence on laminar heat transfer and pretransitional flow i n gas turbines are re-examined in light of these new expressions using our recent thoughts art an ''effective'' frequency of turbulence and an ''effective'' turbulence level. The results of this are that The fr equency moss effective for laminar heat transfer is about 1.3 U/2 pi L -e, where U is the free-stream velocity and L-e is the length scale of the eddies containing rite most turbulent energy, and the most effect ive frequency for producing pretransitional boundary layer fluctuation s is about 0.3 U/2 pi eta, where eta is Kolmogorov's length scale. In addition, the role of turbulence Reynolds number on stagnation heat tr ansfer and transition is discussed and new expressions to account far its effect are provided.