  We present a detailed analytical and numerical study of nonequilibrium
dynamics for the complex Ginzburg-Landau (CGL) equation. In particular, we
characterize evolution morphologies using spiral defects. This paper (referred
to as $\rm I$) is the first in a two-stage exposition. Here, we present
analytical results for the correlation function arising from a single-spiral
morphology. We also critically examine the utility of the Gaussian auxiliary
field (GAF) ansatz in characterizing a multi-spiral morphology. In the next
paper of this exposition (referred to as $\rm II$), we will present detailed
numerical results.
