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The answer and interpretation is fairly simple, Vector upon vector differentiation would look something like this, Where both of these are vectors, __> now remember a vital point, vectors have both magnitude and direction, and can be easily differentiable by time we can easily break the differentiation into parts, and solve for the 2 vectors, ...


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Curl is a measure of the rate at which a(n infinitesimally small) region of fluid rotates about its own centre. You might measure it by inserting a (very) small paddlewheel in the fluid - the speed at which it rotates is the curl. For example, on a fairground Ferris wheel, the big wheel rotates (non-zero curl) the gondolas gyrate (zero curl). Swirl ...


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Suppose you have a 2 dimensional vector field which represents the velocity in a fluid. Let us examine two different cases and calculate the curl of the velocity vector. First, suppose the vector field $\vec{v}$ is given by $$ \vec{v}(x,y,z) = (y,-x,0). $$ If you plot this, we realize that it represents a fluid rotating in the clockwise direction. The curl ...


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Curl is circulation per unit area just like divergence is net flux per unit volume. So any time you care about circulation per area then there you go. Wind farm, vector potentials, magnetic fields, currents.



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