  We present a general systematic formalism for describing dynamics of
fluctuations in an arbitrary relativistic hydrodynamic flow, including their
feedback (known as long-time hydrodynamic tails). The fluctuations are
described by two-point equal-time correlation functions. We introduce a
definition of equal time in a situation where the local rest frame is
determined by the local flow velocity, and a method of taking derivatives and
Wigner transforms of such equal-time correlation functions, which we call
confluent. We find that the equations for confluent Wigner functions not only
resemble kinetic equations, but that the kinetic equation for phonons
propagating on an arbitrary background nontrivially matches the equations for
Wigner functions, including relativistic inertial and Coriolis forces due to
acceleration and vorticity of the flow. We also describe the procedure of
renormalization of short-distance singularities which eliminates cutoff
dependence, allowing efficient numerical implementation of these equations.
