  Galilean and Carrollian algebras acting on two-dimensional Newton-Cartan and
Carrollian manifolds are isomorphic. A consequence of this property is a
duality correspondence between one-dimensional Galilean and Carrollian fluids.
We describe the dynamics of these systems as they emerge from the relevant
limits of Lorentzian hydrodynamics, and explore the advertised duality
relationship. This interchanges longitudinal and transverse directions with
respect to the flow velocity, and permutes equilibrium and out-of-equilibrium
observables, unveiling specific features of Carrollian physics. We investigate
the action of local hydrodynamic-frame transformations in the Galilean and
Carrollian configurations, i.e. dual Galilean and Carrollian local boosts, and
comment on their potential breaking. Emphasis is laid on the additional
geometric elements that are necessary to attain complete systems of
hydrodynamic equations in Newton-Cartan and Carroll spacetimes. Our analysis is
conducted in general Cartan frames as well as in more explicit coordinates,
specifically suited to Galilean or Carrollian use.
