  Spatially inhomogeneous fields of electromagnetic guided modes exhibit a
complex of extraordinary dynamical properties such as the
polarization-dependent transverse momentum, helicity-independent transverse
spin, spin-associated non-reciprocity and unidirectional propagation, etc.
Recently, the remarkable relationship has been established between the spin and
propagation features of such fields, expressed through the spin-momentum
equations [Proc. Natl. Acad. Sci. 118 (2021) e2018816118] connecting the wave
spin with the curl of momentum. Here, the meaning, limitations and specific
forms of this correspondence are further investigated, involving the physically
transparent and consistent examples of paraxial light fields, plane-wave
superpositions and evanescent waves. The conclusion is inferred that the
spin-momentum equation is an attribute of guided waves with well defined
direction of propagation, and it unites the helicity-independent
"extraordinary" transverse spin with the spatially-inhomogeneous longitudinal
field momentum (energy flow) density. Physical analogies with the layered
hydrodynamic flows and possible generalizations for other wave fields are
discussed. The results can be useful in optical trapping, manipulation and the
data processing techniques.
