Between the base of the solar corona at
$r=r_\textrm {b}$
and the Alfvén critical point at
$r=r_\textrm {A}$
, where
$r$
is heliocentric distance, the solar-wind density decreases by a factor
$ \mathop > \limits_\sim 10^5$
, but the plasma temperature varies by a factor of only a few. In this paper, I show that such quasi-isothermal evolution out to
$r=r_\textrm {A}$
is a generic property of outflows powered by reflection-driven Alfvén-wave (AW) turbulence, in which outward-propagating AWs partially reflect, and counter-propagating AWs interact to produce a cascade of fluctuation energy to small scales, which leads to turbulent heating. Approximating the sub-Alfvénic region as isothermal, I first present a brief, simplified calculation showing that in a solar or stellar wind powered by AW turbulence with minimal conductive losses,
$\dot {M} \simeq P_\textrm {AW}(r_\textrm {b})/v_\textrm {esc}^2$
,
$U_{\infty } \simeq v_\textrm {esc}$
, and
$T\simeq m_\textrm {p} v_\textrm {esc}^2/[8 k_\textrm {B} \ln (v_\textrm {esc}/\delta v_\textrm {b})]$
, where
$\dot {M}$
is the mass outflow rate,
$U_{\infty }$
is the asymptotic wind speed,
$T$
is the coronal temperature,
$v_\textrm {esc}$
is the escape velocity of the Sun,
$\delta v_\textrm {b}$
is the fluctuating velocity at
$r_\textrm {b}$
,
$P_\textrm {AW}$
is the power carried by outward-propagating AWs,
$k_\textrm {B}$
is the Boltzmann constant, and
$m_\textrm {p}$
is the proton mass. I then develop a more detailed model of the transition region, corona, and solar wind that accounts for the heat flux
$q_\textrm {b}$
from the coronal base into the transition region and momentum deposition by AWs. I solve analytically for
$q_\textrm {b}$
by balancing conductive heating against internal-energy losses from radiation,
$p\,\textrm {d} V$
work, and advection within the transition region. The density at
$r_\textrm {b}$
is determined by balancing turbulent heating and radiative cooling at
$r_\textrm {b}$
. I solve the equations of the model analytically in two different parameter regimes. In one of these regimes, the leading-order analytic solution reproduces the results of the aforementioned simplified calculation of
$\dot {M}$
,
$U_\infty$
, and
$T$
. Analytic and numerical solutions to the model equations match a number of observations.
A Reliable Iterative Transform Method for Solving an Epidemic Model
