It is convenient to define an eddy of wave number κ as a disturbance containing energy between 0.62 and 1.62. This choice centers the energy around a logarithmic scale, since ln (1.62) ln (1/0.62) 1/2. It also makes the width of the contribution to the spectrum equal to (see Fig. 24.1). The eddy size l is roughly equal to 2π/. This schematic eddy will be used to answer the questions raised earlier.

The energy of an eddy of size 2π/ is roughly proportional to E() times the width of the spectrum, . Thus we can identify a characteristic velocity of this eddy as {E( )} 1/2 . Thus the characteristic strain rate of an eddy of wave number κ is

in the central part of the spectrum. Thus

(24.1)

Thus the strain rate increases with . Note as increases the eddy size decreases. In other words the strain rate increases as eddy size decreases.