F1= -0.64090211;
F2= 0.33867436;
F3= -0.18662854;
CurlyC= 4.0490858;
m1= CurlyC*h^(8/15);
m2= 2 m1 Cos[π/5];
m3= 2 m1 Cos[π/30];
Tc= 2.28919;
α= m1^(1/8) /. h-> h/Tc;
CorrConnected[r_, h_]:=(α^2/π)*(F1^2 BesselK[0, m1*r] + F2^2  BesselK[0, m2*r] + F3^2 BesselK[0, m3*r])

$Assumptions= {r>0, h>0}

CorrConnected[r, h] //Expand

Scaling= CorrConnected[r, r^(-15/8)] /. h-> r^(-15/8) //Simplify