We show that the coronal heating and the acceleration of the fast solar wind in the coronal holes are natural consequence of the footpoint fluctuations of the magnetic fields at the photosphere by one-dimensional , time-dependent , and nonlinear magnetohydrodynamical simulation with radiative cooling and thermal conduction .
We impose low-frequency ( < 0.05 Hz ) transverse photospheric motions , corresponding to the granulations , with velocity \langle dv _ { \perp } \rangle = 0.7 km/s .
In spite of the attenuation in the chromosphere by the reflection , the sufficient energy of the generated outgoing Alfvén waves transmit into the corona to heat and accelerate of the plasma by nonlinear dissipation .
Our result clearly shows that the initial cool ( 10 ^ { 4 } K ) and static atmosphere is naturally heated up to 10 ^ { 6 } K and accelerated to \simeq 800 km/s , and explain recent SoHO observations and Interplanetary Scintillation measurements .