Two-dimensional simulations of strongly anisotropic supernova explosions of a nonrotating 15 solar mass blue supergiant progenitor are presented, which follow the hydrodynamic evolution from times shortly after shock formation until hours later. It is shown that explosions which around the time of shock revival are dominated by low-order unstable modes (i.e. by a superposition of the l=2 and l=1 modes, in which the former is strongest), are consistent with all major observational features of SN 1987A, in contrast to models which show high-order mode perturbations only and were published in earlier work. Among other items, the low-mode models exhibit final iron-group velocities of up to 3300 km/s, strong mixing at the He/H composition interface, with hydrogen being mixed downward in velocity space to only 500 km/s, and a final prolate anisotropy of the ejecta with a major to minor axis ratio of about 1.6. The success of low-mode explosions with an energy of about 2x10**51 erg to reproduce these observed features is based on two effects: the (by 40%) larger initial maximum velocities of metal-rich clumps compared to our high-mode models, and the initial global deformation of the shock. The latter triggers the growth of a strong Richtmyer-Meshkov instability at the He/H interface that results in a global anisotropy of the inner ejecta at late times (i.e. t > 10000 s), although the shock itself has long become spherical by then. The simulations suggest a coherent picture, which explains the observational data of SN 1987A within the framework of the neutrino-driven explosion mechanism using a minimal set of assumptions. It is therefore argued that other paradigms, which are based on (more) controversial physics, may not be required to explain this event. (abbreviated)
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