Gradient of Divergence/Examples/Fluid Density Increase

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Example of Use of Gradient of Divergence

Let $\mathbf V$ be the velocity of a fluid at a point in a region of space $R$.

We have that $\operatorname {div} \mathbf V$ is the scalar rate of change of density with respect to time.

Hence $\grad \operatorname {div} \mathbf V$ gives the magnitude and direction in space of the greatest rate of increase of the space of the density.