Question

This problem is from "A First Course in Turbulence by Hendrik Tennekes and John L. Lumley". I've dedicated lots of hours to solve this exercise.

1.3 The large eddies in a turbulent flow have a length scale t, a velocity scale v()=u, and a time scale te-Yu. The smallest eddies have a length 26 Introduction scale a velocity scale u, and a time scale τ. Estimate the characteristic velocity vir) and the characteristic time tr) of eddies of size r, where r is any length in the range η<r<b Do this by assuming that v(r) and t(r) are determined by and r only. Show that your results agree with the known velocity and time scales at r andr-n. The energy spectrum of turbulence is a plot of E(K) K v (K), where K 1/r is the "wave number" associated with eddies of size r. Find an expression for E(k)

Please explain every thing.
Please write in the paper and then take a high quality photo.

Answer 1

IL KS6