Say I have a quantity I am measuring in time $u=\bar{u}+u'$, where $\bar{u}$ is the mean value and $u'$ is the fluctuating value. How can I find the relationship between $(\bar{u})^2$, $(\bar{u})^3$ and $\overline{u^2}$, $\overline{u^3}$ in terms of $u'/\bar{u}$?
In general, what is the relationship between the mean of the square/cube vs the square/cube of the mean?
