use value of the parameters in [@KBK19]. This gives the values in Table I, where $A_1 \sim K|y^*|^{\zeta_1} C_1$, see Section \[sec:SCT\], and the proportionality factor $K|y^*|^{\zeta_1} = 1/12.952$ is computed at the Reynolds number $15,470$, where the approximated $A_1$ coincides with the measured $A_1$. The $\log$ functions with coefficient $A_1$, from the third column in Table I, and using the constant $B_1$ from the fourth column in Table I, are then compared to the experimental and theoretical values in Fig. \[fig:mean variation\]. The spanwise Townsend-Perry constants, for the spanwise fluctuations, can computed similarly by projecting onto the spanwise lag variable ${\bf t}=(0,t,0).$

In Fig. \[fig:mean variation\] panel (a), the Townsend-Perry constant $A_1$ computed by the SCT does not agree with the measured slope. This was already observed in Ref. [@KBK19], since for low Reynolds numbers the $C_1$s do not provide a good approximation to the $A_1$s. They only do for large Reynolds numbers and the discrepancy (a) occurs at the smallest Reynolds number. This does not happen for the Generalized Townsend-Perry constants, the reasons are explained in Ref. [@KBK19], and for them the $C_p$s, $p \ge 2$, provide good approximations to the $A_p$s for all Reynolds numbers.

  $Re_\lambda$   $C_1$    