Module 7:
Lecture 25: The Energy Cascade (Continued)
 


The energy spectrum is continuous with . For the present discussion, we consider the spectrum to be composed of discreate eddies. The strain rate imposed on an eddy of wave number due to an eddy of next larger size (extending from 0.24 to 0.62 centered around 0.38 in a logarithmic scale) is s (0.38) which will be about from the above relationship. An eddy that is 2 sizes larger than 2π / (energy extending from 0.09 to 0.24 centered around 0.15) once again contributes ½ that of the previous case. Thus we conclude that the total strain rate felt by an eddy at wave number is compraised of ½ from an eddy one size larger, ¼ from an eddy 2-size larger and so on. Therefore most of the energy crossing a given wave number comes from the eddies with slightly smaller wave numbers.