  Turbulence is ever produced in the low-viscosity/large-scale fluid flows by
the velocity shears and, in unstable stratification, by buoyancy forces. It is
commonly believed that both mechanisms produce the same type of chaotic
motions, namely, the eddies breaking down into smaller ones and producing
direct cascade of turbulent kinetic energy and other properties from large to
small scales towards viscous dissipation. The conventional theory based on this
vision yields a plausible picture of vertical mixing and remains in use since
the middle of the 20th century in spite of increasing evidence of the fallacy
of almost all other predictions. This paper reveals that in fact buoyancy
produces chaotic vertical plumes, merging into larger ones and producing an
inverse cascade towards their conversion into the self-organized regular
motions. Herein, the velocity shears produce usual eddies spreading in all
directions and making the direct cascade. This new paradigm is demonstrated and
proved empirically; so, the paper launches a comprehensive revision of the
theory of unstably stratified turbulence and its numerous geophysical or
astrophysical applications.
