  We analyze the stability of g-modes in variable white dwarfs with hydrogen
envelopes. In these stars, the radiative layer contributes to mode damping
because its opacity decreases upon compression and the amplitude of the
Lagrangian pressure perturbation increases outward. The overlying convective
envelope is the seat of mode excitation because it acts as an insulating
blanket with respect to the perturbed flux that enters it from below. A crucial
point is that the convective motions respond to the instantaneous pulsational
state. Driving exceeds damping by as much as a factor of two provided
$\omega\tau_c\geq 1$, where $\omega$ is the radian frequency of the mode and
$\tau_c\approx 4\tau_{th}$ with $\tau_{th}$ being the thermal time constant
evaluated at the base of the convective envelope. As a white dwarf cools, its
convection zone deepens, and modes of lower frequency become overstable.
However, the deeper convection zone impedes the passage of flux perturbations
from the base of the convection zone to the photosphere. Thus the photometric
variation of a mode with constant velocity amplitude decreases. These factors
account for the observed trend that longer period modes are found in cooler
DAVs. The linear growth time, ranging from hours for the longest period
observed modes ($P\approx 20$ minutes) to thousands of years for those of
shortest period ($P\approx 2 $ minutes), probably sets the time-scale for
variations of mode amplitude and phase. This is consistent with observations
showing that longer period modes are more variable than shorter period ones.
Our investigation confirms many results obtained by Brickhill in his pioneering
studies of ZZ Cetis.
