  Signatures of superfluid-like behaviour have recently been observed
experimentally in a nonlinear optical mesh lattice, where the arrival time of
optical pulses propagating in a pair of coupled optical fiber loops is
interpreted as a synthetic spatial dimension. Here, we develop a general theory
of the fluid of light in such optical mesh lattices. On the one hand, this
theory provides a solid framework for an analytical and numerical
interpretation of the experimental observations. On the other hand it
anticipates new physical effects stemming from the specific spatio-temporally
periodic geometry of our set-up. Our work opens the way towards the full
exploitation of optical mesh lattices system as a promising platform for
studies of hydrodynamics phenomena in fluids of light in novel configurations.
