Oil and water being mixed together, a gas bubble forming intricate patterns as it expands in a small gap, a flag flapping or leaf bending in a strong wind ... Each of these involves an interface that separates and interacts with surrounding fluid. All are examples of free-boundary problems, which as a class is one of the most important areas of fluid dynamical research. They are among the most difficult. Mathematically they involve the dynamics of fluids in time-dependent domains, where the domain boundaries can become complex and can exert forces on the fluid. I will lecture on several central, and off-beat, examples of dynamical free boundary problems, focusing especially on the sophisticated numerical methods that have been developed to simulate them, and what these simulations teach us.
