  We use analytic calculations and time-dependent spherically-symmetric
simulations to study the properties of isothermal galactic winds driven by
cosmic-rays (CRs) streaming at the Alfv\'en velocity. The simulations produce
time-dependent flows permeated by strong shocks; we identify a new linear
instability of sound waves that sources these shocks. The shocks substantially
modify the wind dynamics, invalidating previous steady state models: the CR
pressure $p_c$ has a staircase-like structure with $dp_c/dr \simeq 0$ in most
of the volume, and the time-averaged CR energetics are in many cases better
approximated by $p_c \propto \rho^{1/2}$, rather than the canonical $p_c
\propto \rho^{2/3}$. Accounting for this change in CR energetics, we
analytically derive new expressions for the mass-loss rate, momentum flux, wind
speed, and wind kinetic power in galactic winds driven by CR streaming. We show
that streaming CRs are ineffective at directly driving cold gas out of
galaxies, though CR-driven winds in hotter ISM phases may entrain cool gas. For
the same physical conditions, diffusive CR transport (Paper I) yields mass-loss
rates that are a few-100 times larger than streaming transport, and asymptotic
wind powers that are a factor of $\simeq 4$ larger. We discuss the implications
of our results for galactic wind theory and observations; strong shocks driven
by CR-streaming-induced instabilities produce gas with a wide range of
densities and temperatures, consistent with the multiphase nature of observed
winds. We also quantify the applicability of the isothermal gas approximation
for modeling streaming CRs and highlight the need for calculations with more
realistic thermodynamics.
