Vorticity

Vorticity is the curl of a fluid’s velocity field. It describes local spinning and is related to circulation around a small loop per unit area.

Vorticity equation: An evolution equation describing how a fluid’s vorticity changes through advection, stretching, diffusion, and forcing. It states how the field defined by velocity curl evolves in a moving fluid.
Velocity field: A field assigning a velocity vector to each point in space and time. Vorticity is calculated from the spatial variation of this field.
Lamb–Oseen vortex: An axisymmetric viscous vortex whose tangential velocity and vorticity evolve through diffusion. It provides an exact model of a concentrated vortex spreading under viscosity.
Angular velocity: The rate and axis of rotation of a rigid body or rotating frame. A fluid’s vorticity is twice the local angular velocity only for rigid-body rotation.
Rankine vortex: An idealized axisymmetric vortex with solid-body rotation inside a core and potential flow outside. Its distinct core and exterior demonstrate how vorticity can be confined to a region.
Vortex stretching: The amplification or reduction of vorticity when three-dimensional flow stretches or compresses vortex lines. It explains why three-dimensional flows can intensify rotation in ways unavailable to two-dimensional flows.
Curl (mathematics): A vector differential operator measuring the local rotation of a three-dimensional vector field. Applying curl to velocity gives the defining quantity of vorticity.
Taylor–Green vortex: A periodic flow used to study vortex evolution, turbulence, and numerical methods. Its changing vorticity offers a standard test of fluid simulations.
Strain rate: A measure of the rate at which neighboring fluid elements deform relative to one another. Velocity gradients contain both deformation and rotation, while vorticity isolates the antisymmetric part.
Taylor–Couette flow: Flow between concentric rotating cylinders, ranging from laminar motion to complex instabilities. The rotating-cylinder geometry produces measurable shear and vorticity.

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