For turbulent jet, , the linear terms in the equation can be neglected everywhere except near a small boundary layer along the wall. Then neglecting the non-slip conditions at the wall, the solution is given by 
In the case of axisymmetric turbulent plumes where the entrainment rate per unit axial length of the plume increases like , Taylor's solution is given by  where  is a constant,  is the specific buoyancy flux and 
in which  denotes the associated Legendre function of the first kind with degree  and order .