  The atmospheric dynamics of tidally-locked hot Jupiters is characterized by
strong equatorial winds. Understanding the interaction between global
circulation and chemistry is crucial in atmospheric studies and interpreting
observations. Two-dimensional (2D) photochemical transport models shed light on
how the atmospheric composition depends on circulation. In this paper, we
introduce the 2D photochemical (horizontal and vertical) transport model,
VULCAN 2D, which improves on the pseudo-2D approaches by allowing for
non-uniform zonal winds. We extensively validate our VULCAN 2D with analytical
solutions and benchmark comparisons. Applications to HD 189733 b and HD 209458
b reveal a transition in mixing regimes: horizontal transport predominates
below $\sim$0.1 mbar while vertical mixing is more important at higher
altitudes above 0.1 mbar. Motivated by the previously inferred carbon-rich
atmosphere, we find that HD 209458 b with super-solar carbon-to-oxygen ratio
(C/O) exhibits pronounced C$_2$H$_4$ absorption on the morning limb but not on
the evening limb, owing to horizontal transport from the nightside. We discuss
when a pseudo-2D approach is a valid assumption and its inherent limitations.
Finally, we demonstrate the effect of horizontal transport in transmission
observations and its impact on the morning-evening limb asymmetry with
synthetic spectra, highlighting the need to consider global transport when
interpreting exoplanet atmospheres.
