Incompressible Flow

A fluid, gas or plasma is said to be incompressible if

$$\nabla \cdot {\bf v} = 0.$$ (2.7)

Thus, the density of a fluid element does not vary as it moves with the flow so that

$${D\rho \over Dt} = 0.$$ (2.8)

$\nabla \cdot {\bf v} \ne 0$ implies that the fluid is compressible.