  We present a derivation that begins with the Navier--Stokes equation and ends
with a prediction of multiple statistically stable states identical to those
observed in a spanwise rotating plane Couette flow. This derivation is able to
explain the presence of multiple states in fully developed turbulence and the
selection of one state over the other by differently sized computational
domains and different initial conditions. According to the present derivation,
two and only two statistically stable states are possible in an infinitely
large plane Couette flow with spanwise rotation, and that multiple states are
not possible at very slow or very rapid rotation speeds. We also show the
existence of limit cycles near statistically stable states.
