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For a sinusoidal plane wave propagating along axis the orbital angular momentum density vanishes.
The angular momentum density vector is given by a vector product as in classical mechanics:
The angular momentum density of a fluid element is written either as an antisymmetric tensor () or, equivalently, as a pseudovector.
For continua or fields, mass density replaces mass to obtain an angular momentum density, then the total angular momentum in a volume is the volume integral over the volume.
The angular momentum of a fluid element can be separated into extrinsic angular momentum density due to the flow () and intrinsic angular momentum density due to the rotation of the fluid particles about their center of mass ():
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