  For the constant-stress layer of wall turbulence, two-point correlations of
velocity fluctuations are studied theoretically by using the attached-eddy
hypothesis, i.e., a phenomenological model of a random superposition of
energy-containing eddies that are attached to the wall. While the previous
studies had invoked additional assumptions, we focus on the minimum assumptions
of the hypothesis to derive its most general forms of the correlation
functions. They would allow us to use or assess the hypothesis without any
effect of those additional assumptions. We also study the energy spectra and
the two-point correlations of the rate of momentum transfer and of the rate of
energy dissipation.
