Math Insight

Image: Microscopic circulation is induced by changes of the vector field

Microscopic circulation is induced by changes of the vector field The circle with center fixed will tend to rotate in a counterclockwise direction if $\dlvfc_2$ (in red) is larger to its right or if $\dlvfc_1$ (in blue) is larger below. This picture gives intuition why changes in the vector field components lead to circulation and that the formula for microscopic circulation is $\pdiff{\dlvfc_2}{x}-\pdiff{\dlvfc_1}{y}$.

Image file: microscopic_circulation_vector_field_change.png

Source image file: microscopic_circulation_vector_field_change.svg
Source image type: Inkscape SVG

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