  We propose and analyze the perfectly matched layer (PML) method for the
time-harmonic acoustic waves driven by the white noise source in the presence
of the uniform flow. A PML is an artificial absorbing layer commonly used to
truncate computational regions to solve problems in unbounded domains. We study
a modification of PML method based on B\'ecache et. al. A truncated domain
problem for stochastic convected Helmholtz equation in the infinite duct is
constructed by applying PMLs. Our PML method omits the instability of inverse
upstream modes in the PML. Moreover, a suitable jump condition on boundaries
between computational domain and PMLs is not required. We analyze the
stochastic error generated by truncations of the domain. Thus the convergence
analysis of the solution is provided in the sense of mean-square.
