Helmholtz's theorem

Helmholtz's theorem states that a smooth, divergence-free vector field in three-dimensional space can be uniquely represented as the sum of an irrotational (curl-free) part and a solenoidal (divergence-free) part. In practical terms, this means that any flow, like water or air, can be understood as a combination of swirling motion and uniform movement. This theorem is important in fields like fluid dynamics and electromagnetism, where understanding the different components of a field can help in analyzing and predicting behavior in physical systems.