Consider a two-point velocity correlation tensor for homogeneous turbulence
For isotropic turbulence, this correlation tensor can be expressed in terms of two scalar functions, using the invariant theory of full rotation group, first derived by Howard P. Robertson in 1940,
where  is the root mean square turbulent velocity and  are turbulent velocity in all three directions. Here,  is the longitudinal correlation and  is the lateral correlation of velocity at two different points. From continuity equation, we have
Thus  uniquely determines the two-point correlation function. Theodore von Kármán and Leslie Howarth derived the evolution equation for  from Navier–Stokes equation as
where  uniquely determines the triple correlation tensor