Solenoidal vector field

A vector field whose divergence vanishes everywhere in its domain. Its flux has no local sources or sinks, though the field need not vanish or be globally expressible as a curl.

Divergence: A scalar measure of a vector field’s net outward flow per unit volume at each point. A solenoidal field is defined by divergence being zero at every point.
Continuity equation: A local conservation law relating a changing density to the divergence of its flux. For constant density, this conservation law reduces to zero divergence of velocity.
Vector field: A function assigning a vector to each point in a domain. Solenoidality is a constraint on a vector field, not a separate kind of quantity.
Irrotational vector field: A vector field whose curl vanishes throughout its domain. Zero curl constrains circulation, whereas solenoidality constrains divergence.
Gauss's theorem: A theorem equating the flux through a closed surface to the volume integral of divergence inside it. Zero divergence makes the net flux through every suitable closed surface vanish.
Navier–Stokes equations: Partial differential equations governing the motion of viscous fluids. Incompressible Navier–Stokes models impose a solenoidal velocity field.
Divergence theorem: A theorem relating the integral of divergence over a volume to flux across its boundary. It turns the pointwise zero-divergence condition into a statement about boundary flux.
Conservative vector field: A vector field expressible as the gradient of a scalar potential. A gradient field is not generally divergence-free; its divergence is the potential’s Laplacian.
Vector potential: A vector field whose curl equals a specified vector field. Locally, a divergence-free field can be represented as the curl of a vector potential.
Magnetic field: A vector field describing magnetic influence and forces on moving charges and magnetic materials. Gauss’s law for magnetism states that the magnetic field has zero divergence.

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Gauss's law for magnetismRelated: In ordinary electromagnetism, the magnetic field is solenoidal by this law.