  Incorporating probabilistic terms in mathematical models is crucial for
capturing and quantifying uncertainties of real-world systems. However,
stochastic models typically require large computational resources to produce
meaningful statistics. For such reason, the development of reduction techniques
becomes essential for enabling efficient and scalable simulations of complex
scenarios while quantifying the underlying uncertainties. In this work, we
study the accuracy of Polynomial Chaos (PC) surrogate expansion of the
probability space on a bifurcating phenomena in fluid dynamics, namely the
Coand\u{a} effect. In particular, we propose a novel non-deterministic approach
to generic bifurcation problems, where the stochastic setting gives a different
perspective on the non-uniqueness of the solution, also avoiding expensive
simulations for many instances of the parameter. Thus, starting from the
formulation of the Spectral Stochastic Finite Element Method (SSFEM), we extend
the methodology to deal with solutions of a bifurcating problem, by working
with a perturbed version of the deterministic model. We discuss the link
between the deterministic and the stochastic bifurcation diagram, highlighting
the surprising capability of PC polynomials coefficients of giving insights on
the deterministic solution manifold.
