Vorticitet

Vorticitet, or vorticity, is a property of a fluid that describes the local spinning motion of fluid elements. It is defined as the curl of the velocity field: ω = ∇ × v. In three dimensions, ω is a vector whose direction indicates the axis of rotation and whose magnitude corresponds to twice the angular speed of the element. In two-dimensional flows, the vorticity reduces to a single scalar component perpendicular to the plane, ωz = ∂v/∂x − ∂u/∂y.

Vorticity is transported by the flow and is affected by viscosity. In an incompressible, Newtonian fluid, the vorticity evolution is given by ∂ω/∂t = ∇ × (v × ω) + ν ∇^2 ω, where ν is the kinematic viscosity. In inviscid flow (ν = 0) and with certain conditions, circulation around a material loop is conserved (Kelvin’s circulation theorem).

Vorticity can be generated by misaligned gradients of density and pressure (baroclinic torque) and by boundary effects, such as shear at solid walls, which inject vorticity into the flow. It is advected and diffused, leading to structures called vortices.

Applications of vorticity span meteorology, oceanography, aerodynamics, and engineering. Vorticity fields are commonly measured by techniques such as particle image velocimetry and other velocity-field methods. Understanding vorticity helps explain wake turbulence, lift generation, and mixing processes.