  Investigation of physics on two-dimensional curved surface has significant
meaning in study of general relativity, inasmuch as its realizability in
experimental analogy and verification of faint gravitational effects in
laboratory. Several phenomena about dynamics of particles and electromagnetic
waves have been explored on curved surfaces. Here we consider Wolf effect, a
phenomenon of spectral shift due to the fluctuating nature of light fields, on
an arbitrary surface of revolution (SOR). The general expression of the
propagation of partially coherent beams propagating on arbitrary SOR is derived
and the corresponding evolution of light spectrum is also obtained. We
investigate the extra influence of surface topology on spectral shift by
defining two quantities, effective propagation distance and effective
transverse distance, and compare them with longitudinal and transverse proper
lengths. Spectral shift is accelerated when the defined effective quantities
are greater than real proper lengths, and vice versa. We also employ some
typical SORs, cylindrical surfaces, conical surfaces, SORs generated by power
function and periodic peanut-shell shapes, as examples to provide concrete
analyses. This work generalizes the research of Wolf effect to arbitrary SORs,
and provides a universal method for analyzing properties of propagation
compared with that in flat space for any SOR whose topology is known.
