The concept of universality has played an important role in shaping ourunderstanding of turbulent flows. However,it is well established that universality in most turbulent flows is highly compromised by the finitenessof the Reynoldsnumber. In that case, the turbulent motion is flow dependent and boundary or initial conditions can have an effecton all scales. Specifically, for turbulent free shear flows, the turbulent motion is very different across the flow andstatistics may depart significantly from classical theories.In this presentation, the combined effect of internal and external intermittency on the statistical properties of small-scale turbulence is investigated in a temporally evolving, planar turbulent jet flow. In turbulent jet flows, the phenomenon of external intermittency originates from a very thin layer, known as turbulent/non-turbulent interface, that separates the inner turbulent core from the outer irrotational surrounding fluid. The impact of external intermittency on small-scale turbulence is studied across the jet by the self-similarity of velocitystructure functions. It is shown that the scaling of structure functions exhibits a growing departure from the prediction of classical scaling solutions toward the edge. Empirical evidence is provided that this departure is primarily due to external intermittency and the associated break-down of self-similarity.In the next step, the analysisis applied tothe mixture fraction field of a turbulent non-premixedflame. In non-premixed flames,the zone of chemical reaction is locatedclose to the turbulent/non-turbulent interface. Understanding the turbulent fluctuations in that region of the flow hastherefore strong implications for turbulent mixing between fuel and oxidizer as well as thecombustionprocess