Abstract
The kinetics of single-species annihilation, 
, is investigated in which each particle has a fixed velocity which may be either 
with equal probability, and a finite diffusivity. In one dimension, the interplay between convection and diffusion leads to a decay of the density which is proportional to 
. At long times, the reactants organize into domains of right- and left-moving particles, with the typical distance between particles in a single domain growing as 
, and the distance between domains growing as t. The probability that an arbitrary particle reacts with its nth neighbour is found to decay as 
for same-velocity pairs and as 
for +- pairs. These kinetic and spatial exponents and their interrelations are obtained by scaling arguments. Our predictions are in excellent agreement with numerical simulations.