  In this paper, we study two-dimensional steady incompressible Euler flows in
which the vorticity is sharply concentrated in a finite number of regions of
small diameter in a bounded domain. Mathematical analysis of such flows is an
interesting and physically important research topic in fluid mechanics. The
main purpose of this paper is to prove that in such flows the locations of
these concentrated blobs of vorticity must be in the vicinity of some critical
point of the Kirchhoff-Routh function, which is determined by the geometry of
the domain. The vorticity is assumed to be only in $L^{4/3},$ which is the
optimal regularity for weak solutions to make sense. As a by-product, we prove
a nonexistence result for concentrated multiple vortex flows in convex domains.
