The energy absorbed by eddies of next smaller size (extending from 1.6 to 4.2 centered around 2.6) is about

(25.3)

This follows from . Thus

Since

Similarly the energy absorbed by an eddy that is next smaller size (extending from 4.2 to 11 centered around 6.76) is

Thus the sum of energies absorbed by eddies smaller than wave number k from eddies of wave number larger than is

Thus we conclude that eddies of wave number receive about 2/3 of the total energy transfer, those of the next smaller size receive 1/6 th and all further smaller eddies combined also receive about 1/6 th .

Thus the following picture emerges. Most of the energy that is exchanged across a given wave number apparently comes mostly from the next larger eddies and goes to the next smaller eddies. It seems reasonable to describe the energy transfer as a cascade, very much like a series of water falls, each one filling a pool that overflows into the next one below. This picture is exceptionally useful; since the largest eddies and the smallest eddies clearly have very little effect on the energy transfer at intermediate wave numbers.

It is also useful to remember two things in connection with the above description:

• It is rather a leaky cascade since half the water crossing a given level comes directly not from the one immediately above it, but all the other pools uphill; and
  
• It ignores viscosity.