Velocity spectra in the irrotational flow outside a turbulent shear layer

The relationship between the spectra of the three normal stresses near a turbulent shear layer is derived from the constraint of irrotationality. The relationship implies that the common practice of determining time scales of the turbulence from spectra in the near field is not valid. This implication is reinforced by a discussion of the scaling of irrotational spectra that follows from the formulation of Phillips (1975).