Constraints on the invariant functions of axisymmetric turbulence

Constraints are derived for the two invariant functions Q₁ and Q₂ that occur in Chandrasekhar’s development of the axisymmetric turbulence theory. These constraints must be satisfied for the correlation tensor derived from Q₁ and Q₂ to be that of a stationary random process, i.e., for the turbulence to be realizable. The equivalent results in spectrum space are also developed. Applications of the constraints in aerodynamic noise modeling are discussed. It is shown that significant errors in prediction can be introduced by the use of turbulence models which violate the constraints.