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Definition
The azimuthal velocity component tangent to circles around the chosen axis.
The swirl component is the scalar in cylindrical coordinates
Its vector contribution is tangent to circles about the chosen axis. A flow is without swirl when .
Away from the -axis, cylindrical coordinates are
The angle in radians is taken modulo , or on a local angular interval. The corresponding orthonormal frame is
Its angular derivatives are and .
For , the angular velocity of a fluid about the -axis is the swirl velocity divided by radius:
Along a particle trajectory away from the axis, . Its units are inverse time when the angle is measured in radians.
The specific angular momentum about the -axis is
“Specific” means per unit mass. It differs from the angular velocity by the factor .