When a vessel containing particles is subjected to vertical vibrations with an acceleration greater than 1 g, a convection mode of particles appears : particles move downward along the vertical side walls and upward in the middle, forming a heap. With the increase in vibrational intensity another convection mode sets in, wherein particles move upward along the vertical side walls and downward in the middle, forming a valley. The latter convection mode is stable enough to yield multiple pairs of convection rolls with a further increase in vibrational acceleration, showing strong nonlinearity of the system.