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Internal (inertial) waves in a uniformly stratified (rotating) fluid obey a highly specific dispersion relation that admits their propagation in form of oblique beams, which preserve their inclination to the distinguished direction (prescribed by gravity for internal waves and the angular velocity vector for the inertial waves) upon reflection. In confined domains with sloping walls, repeated reflections of the wave beams lead to concentration of the wave energy at closed loops called wave attractors. The dynamics of wave attractors is best studied in essentially two-dimensional problems (plane or axisymmetric), progressing from the ideal-fluid concept to more realistic ones, with consideration of viscous effects, energy balance and cascades of wave-wave interactions. Development of fully three-dimensional highly nonlinear regimes has not yet been unexplored. The present paper considers direct numerical simulations of …