  The alignment of a pair of spherical particles perpendicular to a
horizontally oscillating flow is attributed to a non-zero residual flow, known
as steady streaming. This phenomenon is the basis of complex patterns in denser
systems, such as particle chains and the initial stages of rolling-grain
ripples. Previous studies on such self-organization processes used two distinct
systems: an oscillating box filled with viscous fluid and an oscillating
channel flow, where the fluid oscillates relative to the bottom boundary. In
this paper, we show that particle pair dynamics in these two systems are
fundamentally different, due to the presence of a Stokes boundary layer above
the bottom in the oscillating channel flow. The results are obtained from
direct numerical simulations in which the dynamics of a pair of particles are
simulated using an immersed boundary method. The oscillating box and the
oscillating channel flow are only equivalent in a limited region of the
parameter space, where both the normalized Stokes boundary layer thickness and
the normalized relative particle excursion length are small. Overall, the
particle dynamics in the oscillating channel flow, compared to the oscillating
box, are governed by an additional dimensionless parameter.
