  We examine the anisotropies in the power spectrum by the mapping of real to
redshift space. Using the Zel'dovich approximation, we obtain an analytic
expression for the nonlinear redshift space power spectrum in the distant
observer limit. For a given unbiased galaxy distribution in redshift space, the
anisotropies in the power spectrum depend on the parameter $f(\Omega)\approx
\Omega^{0.6}$, where $\Omega$ is the density parameter. We quantify these
anisotropies by the ratio, $R$, of the quadrupole to monopole angular moments
of the power spectrum. In contrast to linear theory, the Zel'dovich
approximation predicts a decline in $R$ with decreasing scale. This departure
from linear theory is due to nonlinear dynamics and not a result of incoherent
random velocities. The rate of decline depends strongly on $\Omega$ and the
initial power spectrum. However, we find a {\it universal} relation between the
quantity $R/R_{lin}$ (where $R_{lin}$ the linear theory value of $R$) and the
dimensionless variable $k/k_{nl}$, where $k_{nl}$ is a wavenumber determined by
the scale of nonlinear structures. The universal relation is in good agreement
with a large N-body simulation. This universal relation greatly extends the
scales over which redshift distortions can be used as a probe of $\Omega$. A
preliminary application to the 1.2 Jy IRAS yields $\Omega\sim 0.4$ if IRAS
galaxies are unbiased.
