  Compact white dwarf (WD) binaries are important sources for space-based
gravitational-wave (GW) observatories, and an increasing number of them are
being identified by surveys like ZTF. We study the effects of nonlinear
dynamical tides in such binaries. We focus on the global three-mode parametric
instability and show that it has a much lower threshold energy than the local
wave-breaking condition studied previously. By integrating networks of coupled
modes, we calculate the tidal dissipation rate as a function of orbital period.
We construct phenomenological models that match these numerical results and use
them to evaluate the spin and luminosity evolution of a WD binary. While in
linear theory the WD's spin frequency can lock to the orbital frequency, we
find that such a lock cannot be maintained when nonlinear effects are taken
into account. Instead, as the orbit decays, the spin and orbit go in and out of
synchronization. Each time they go out of synchronization, there is a brief but
significant dip in the tidal heating rate. While most WDs in compact binaries
should have luminosities that are similar to previous traveling-wave estimates,
a few percent should be about ten times dimmer because they reside in heating
rate dips. This offers a potential explanation for the low luminosity of the CO
WD in J0651. Lastly, we consider the impact of tides on the GW signal and show
that LISA and TianGO can constrain the WD's moment of inertia to better than 1%
for deci-Hz systems.
