We study long-range order in two dimensions where an order parameter is
advected by linear laminar flows. The linear laminar flows include three
classes: rotational, shear, and elongational flows. Under these flows, we
analyze an ordered state of the O(N) scalar model in the large-N limit. We
show that the stability of the ordered state depends on the flow pattern; the
shear and elongational flows stabilize but the rotational flow does not. We
discuss a physical interpretation of our results based on interaction
representation in quantum mechanics. The origin of the long-range order is
interpreted from the advection of wavenumbers along the streamlines and its
stretching effect stabilizes the order.Comment: 6+5pages, 3+1figure