Constraints on the invariant functions of axisymmetric turbulence

Constraints are derived for the two invariant functions Q1 and Q2 that occur in Chandrasekhar's (1950) 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.