Flow-induced actions on cylinders in statistically-symmetric cross flow

The measurements carried out during aerodynamic tests are usually (if the Reynolds number is large) interpreted as realisations of random processes. Typical tests consider a cylinder exposed to the flow in a nominally-symmetric configuration (e.g. symmetric cylinders with zero angle-of-attack). In such a condition, the pressure field and the fluid-induced loads (forces and torque) acting on the cylinder are expected to fulfil some statistical symmetry condition, as has been documented by several researchers. In particular, it was experimentally observed that the cross-wind force and the torsional moment tend to have zero mean value and to be substantially uncorrelated with respect to the along-wind force. Small (but non-null) correlation or coherence values were often reported and it is not clear whether or not they should be treated as experimental imperfections or whether they are rather the trace of some physical phenomenon. With the objective of clarifying the above-mentioned problem, the present paper introduces the concept of statistically-symmetric random process, proposing a definition in which the symmetry constraint is imposed on the characteristic functional of the pressure field. Consequent conditions on the statistical moments and on the covariance eigenfunctions of the aerodynamic actions are derived accordingly. A numerical procedure aimed at correcting measured data to impose a rigorous second-order statistical symmetry is presented and applied on pressure measurements carried out in a wind-tunnel test.