Definition:Solenoidal Vector Field

Definition

Let $\mathbf V$ be a vector field acting over a region of space $R$.

Definition 1

$\mathbf V$ is defined as being solenoidal if and only if its divergence is everywhere zero:

$\operatorname {div} \mathbf V = 0$

Definition 2

$\mathbf V$ is defined as being solenoidal if and only if lines of flux form closed curves.

Also see

• Equivalence of Definitions of Solenoidal Vector Field

• Results about solenoidal vector fields can be found here.

Linguistic Note

The word solenoidal derives from a Greek word meaning tube.

Sources

• 1951: B. Hague: An Introduction to Vector Analysis (5th ed.) ... (previous) ... (next): Chapter $\text {V}$: Further Applications of the Operator $\nabla$: $7$. The Classification of Vector Fields