Contour advection

Contour advection is a Lagrangian method of simulating the evolution of one or more contours or isolines of a tracer as it is stirred by a moving fluid. Consider a blob of dye injected into a river or stream: to first order it could be modelled by tracking only the motion of its outlines. It is an excellent method for studying chaotic mixing: even when advected by smooth or finitely-resolved velocity fields, through a continuous process of stretching and folding, these contours often develop into intricate fractals. The tracer is typically passive as in but may also be active as in, representing a dynamical property of the fluid such as vorticity. At present, advection of contours is limited to two dimensions, but generalizations to three dimensions are possible.