In this work we focus on reducing the wall clock time required to compute statistical estimators of highly chaotic incompressible flows on high performance computing systems. Our approach consists of replacing a single long-term simulation by an ensemble of multiple independent realizations, which are run in parallel with different initial conditions. A failure probability convergence criteria must be satisfied by the statistical estimator of interest to assess convergence. Its error analysis leads to the identification of two error contributions: the initialization bias and the statistical error. We propose an approach to systematically detect the burn-in time in order to minimize the initialization bias, accompanied by strategies to reduce simulation cost. The framework is validated on two very high Reynolds number obstacle problems of wind engineering interest in a high performance computing environment.