  We study the growth of the explosion energy after shock revival in
neutrino-driven explosions in two and three dimensions (2D/3D) using
multi-group neutrino hydrodynamics simulations of an $11.2 M_\odot$ star. The
3D model shows a faster and steadier growth of the explosion energy and already
shows signs of subsiding accretion after one second. By contrast, the growth of
the explosion energy in 2D is unsteady, and accretion lasts for several seconds
as confirmed by additional long-time simulations of stars of similar masses.
Appreciable explosion energies can still be reached, albeit at the expense of
rather high neutron star masses. In 2D, the binding energy at the gain radius
is larger because the strong excitation of downward-propagating g-modes removes
energy from the freshly accreted material in the downflows. Consequently, the
mass outflow rate is considerably lower in 2D than in 3D. This is only
partially compensated by additional heating by outward-propagating acoustic
waves in 2D. Moreover, the mass outflow rate in 2D is reduced because much of
the neutrino energy deposition occurs in downflows or bubbles confined by
secondary shocks without driving outflows. Episodic constriction of outflows
and vertical mixing of colder shocked material and hot, neutrino-heated ejecta
due to Rayleigh-Taylor instability further hamper the growth of the explosion
energy in 2D. Further simulations will be necessary to determine whether these
effects are generic over a wider range of supernova progenitors.
