A modelling methodology to reproduce the experimental measurements of a turbulent flow in the presence of symmetry is presented. The flow is a three-dimensional wake generated by an axisymmetric body. We show that the dynamics of the turbulent wake flow can be assimilated by a nonlinear two-dimensional Langevin equation, the deterministic part of which accounts for the broken symmetries that occur in the laminar and transitional regimes at low Reynolds numbers and the stochastic part of which accounts for the turbulent fluctuations. Comparison between theoretical and experimental results allows the extraction of the model parameters.