Turbulence drastically enhances mixing rates. Sometimes, that is all we need to model, and we can ignore the small scales. Other times, however, the small whirls strongly affect the large ones and the multi-scale nature of turbulence fully unfolds, challenging all efforts to describe it in simple ways. This is where supercomputing comes into play. Supercomputing has given us the opportunity to study turbulence with unprecedented accuracy, providing a new avenue to solve long-standing problems in science and engineering. This project considers some of these problems.