Representation of Isotropic Turbulence by Scalar Functions

The maximum number N(n) of scalar functions of wavevector needed to represent the general cumulant of order n of isotropic turbulence is determined. In addition to reproducing the known results that N(2) = 1, N(3) = 2, it is shown that N(4) = 4, N(5) = 4, N(6) = 9, etc.