  We experimentally investigate the effects of parametric instabilities on the
short-time heating process of periodically-driven bosons in 2D optical lattices
with a continuous transverse (tube) degree of freedom. We analyze three types
of periodic drives: (i) linear along the x-lattice direction only, (ii) linear
along the lattice diagonal, and (iii) circular in the lattice plane. In all
cases, we demonstrate that the BEC decay is dominated by the emergence of
unstable Bogoliubov modes, rather than scattering in higher Floquet bands, in
agreement with recent theoretical predictions. The observed BEC depletion rates
are much higher when shaking both along x and y directions, as opposed to only
x or only y. This is understood as originating from the interaction-induced
non-separability along the two lattice directions. We also report an explosion
of the heating rates at large drive amplitudes, and suggest a phenomenological
description beyond Bogoliubov theory. In this strongly-coupled regime, circular
drives heat faster than diagonal drives, which illustrates the non-trivial
dependence of the heating on the choice of drive.
