what is the significance of positive and negative divergence of a vector field
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The divergence of the above vector field is positive since the flow is expanding. In contrast, the below vector field represents fluid flowing so that it compresses as it moves toward the origin. Since this compression of fluid is the opposite of expansion, the divergence of this vector field is negative.
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Both the divergence and curl are vector operators whose properties are revealed by viewing a vector field as the flow of a fluid or gas. Here we focus on the geometric properties of the divergence; you can read a similar discussion of the curl on another page.
The divergence of a vector field is relatively easy to understand intuitively. Imagine that the vector field F pictured below gives the velocity of some fluid flow. It appears that the fluid is exploding outward from the origin.
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