[8cold8hot]

Dear all,
I am reading "Turbulent Flows" which is written by Pope, the filtered kinetic energy on Page 585 confuses me as the Exercise 13.22 says that <filtered E> can be integrated over all k of the spectrum E(k) multiplied by 1. However, I think the integration results in the kinetic energy k. I suppose that In order to obtain the filtered kinetic energy, it shall be integrated over all k of the spectrum E(k) multiplied by G(k) otherwise the filtered kinetic energy and the kinetic energy will be exactly the same.
Am I making anything wrong in this procedure?
Thanks.