Streamfunction

Definition

The Streamfunction ($\\psi$) is a scalar function used in two-dimensional incompressible flow. Its value is constant along streamlines.

Formula

$u = \\frac{\\partial\\psi}{\\partial y}, \quad v = -\\frac{\\partial\\psi}{\\partial x}$ This definition automatically satisfies the continuity equation $\\nabla\\cdot\\mathbf{v} = 0$.

Relationships

• Related: Velocity Potential, Continuity Equation