  In this work, we present the longest photometric monitoring of up to 1200
hours of the strongly variable brown-dwarf binaries Luhman 16 AB and provide
evidence of $\pm$5% variability on a timescale of several-to-hundreds of hours
for this object. We show that short-period rotational modulation around 5 hours
(k = 1 wavenumber) and 2.5 hours (k = 2 wavenumber) dominate the variability
under 10 hours, where the planetary-scale waves model composed of k = 1 and k =
2 waves provides good fits to both the periodogram and light curve. In
particular, models consisting of three to four sine waves could explain the
variability of light curve durations up to 100 hours. We show that the relative
range of k = 2 periods is narrower compared to k = 1 period. Using simple
models of zonal banding in Solar System giants, we suggest that the difference
in period range arises from the difference in windspeed distribution at low and
mid-to-high latitudes in the atmosphere. Lastly, we show that Luhman 16 AB also
exhibits long-period $\pm$5% variability with periods ranging from 15 hours up
to 100 hours over the longest monitoring of this object. Our results on k = 1
and k = 2 waves and long-period evolution are consistent with previous 3D
atmosphere simulations, demonstrating that both latitude-dependent waves and
slow-varying atmospheric features are potentially present in Luhman 16 AB
atmospheres and are significant contribution to the light curve modulation over
hundreds of rotations.
