 Stream function

A two-dimensional incompressible velocity field can be written either as $u={\psi }_y$, $v=-{\psi }_x$ or with both signs reversed. The continuity equation then holds identically.

A stream function is a mathematical tool used in fluid mechanics to describe the flow of incompressible fluids. It is a scalar function whose contours represent the flow lines of the fluid. When the flow is two-dimensional, the stream function can help visualize the flow, as the flow velocity components can be obtained from this function. ### Key Characteristics of Stream Functions: 1. **Incompressible Flow**: Stream functions are primarily used for incompressible flow scenarios.