  Phase transition dynamics may play important roles in the evolution history
of the early universe, such as its possible roles in electroweak baryogenesis
and dark matter.We systematically discuss and clarify the important details of
the phase transition dynamics during a strong first-order phase transition
(SFOPT). We classify the SFOPT into four types: slight supercooling, mild
supercooling, strong supercooling, and ultra supercooling. Using different
characteristic temperatures, length scales and bubble wall velocities, the
corresponding gravitational wave (GW) spectra are investigated in details. We
emphasize the essential importance of using the correct characteristic
temperature and length scale when the phase transition dynamics and GW spectra
are calculated. Especially, for strong supercooling and ultra supercooling
cases, there are obvious differences of the phase transition strength and GW
spectra between the results calculated at the nucleation temperature and those
derived at the percolation temperature. For ultra supercooling case, we propose
a criterion to quantify whether the phase transition can terminate. Besides the
model-independent discussions, we also study three representative models as
concrete examples to clearly show the subtle points therein.
