A theory is presented where the weakly nonlinear analysis of laminar g lobally unstable flows in the presence of external forcing is extended to the turbu lent regime. The analysis is demonstrated and validated using experimental results of an axis ymmetric bluff body wake at high Reynolds numbers, Re D ∼ 1 . 88 × 10 5 , where forcing is applied using a Zero-Net-Mass-Flux actuator located at the base of the blunt bo dy. In this study we focus on the response of antisymmetric coherent structures wit h azimuthal wavenumbers m = ± 1 at a frequency St D = 0 . 2, responsible for global vortex shedding. We found experimentally that axisymmetric forcing ( m = 0) couples nonlinearly with the global shedding mode when the flow is forced at twice the shedding frequen cy, resulting in parametric subharmonic resonance through a triadic interaction b etween forcing and shedding. We derive simple weakly nonlinear models from the phase-av eraged Navier- Stokes equations and show that they capture accurately the obs erved behaviour for this type of forcing. The unknown model coefficients are obtained e xperimentally by producing harmonic transients. This approach should be applicable in a variety of turbulent flows to describe the response of global modes to forcin g.