Motivation for some operators in the dyadic model of Navier Stokes equation

Question

What's the motivation for cascade operator $C_{u}, C_{d}$ (and then the dyadic version of operator $B=(u\cdot \nabla)u$), which is

$(C_{u}(u,v))_{Q} = 2^{\frac{5}{2}j}u_{\tilde{Q}}v_{\tilde{Q}}$,

$(C_{d}(u,v))_{Q} = 2^{\frac{5}{2}(j+1)}u_{Q}(\Sigma_{Q'\in C^1(Q)}v_{Q'})$he

where $j = j(Q)$,$\tilde{Q}$ is the unique parent of $Q$, $C^1(Q)$ is the set of children of $Q$

then dyadic version of $B$ is defined as

$B = C_{u}-C_{d}$

in the dyadic model of Navier Stokes equation?

Thanks for help!