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.