= Finite-edge stress condition for a mixing-length jet
For a symmetric localized <turbulent plane jet similarity> profile, integrated momentum balance gives $ff'=2C_1^2\eta^2(f'')^2$ on $\eta>0$. At a finite free edge $\eta_w>0$, $f'(\eta_w)=0$ and finite $f(\eta_w)$ force $f''(\eta_w)=0$. Thus the <mixing length> model $l=C_1|y|$ cannot simultaneously impose zero velocity and a nonzero maximum velocity gradient at the edge. Its <eddy viscosity> vanishes there. Moreover, a nonzero finite centreline speed $f'(0)=a$ forces $|f''|\sim a/(\sqrt2C_1\sqrt\eta)$ near the centre, displaying a singular-shear defect of that local closure. The molecular-viscosity neglect cannot be uniform in this core.
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