A bowed string behaves differently because the string has a
continuous source of energy, so the player can maintain a
note indefinitely until they stop bowing. Also, plucking the
string makes the harmonic quickly fade leaving behind the
fundamental and lower, weak harmonics while bowing continues
the harmonic spectrum.
The motion of the string from the bow is driven by static
friction, sticking of the bow, and kinetic friction, sliding
of the bow. The static friction is high while the sliding
friction is low which causes the bow to stick to the string,
dragging the string with it. This causes a kink to move in
the string and reflect off the fixed end. When it returns to
the contact point, it breaks free of the bow and slides past
with little friction, which is the slip phase of motion.
Then its momentum carries on and it reverses direction
traveling to the other fixed end of the string. Then it
catches the bow again and restarts the cycle, thus the cycle
of stick and slip on the bow has the same period as the
vibration of the string.
This makes the bowing harmonics more complicated. For
example, for the second harmonic there are two cycles of
stick/slip in the time that the kink makes a full trip up
and down the string. There are always two kinks traveling
along the string, at L/2 apart. Each time it returns to the
bow from returning from far end of string, it initiates a
slip, when returning from the close end of the string, it
initiates a stick. The fundamental and second harmonic
cycles of a bowed string are shown below:
Photos from the University New South Wales