  The dynamics of spectral transport in two-dimensional turbulent convection of
electrically conducting fluids is studied by means of direct numerical
simulations (DNS) in the frame of the magnetohydrodynamic (MHD) Boussinesq
approximation. The system performs quasi-oscillations between two different
regimes of small-scale turbulence: one dominated by nonlinear MHD interactions,
the other governed by buoyancy forces. The self-excited change of turbulent
states is reported here for the first time. The process is controlled by the
ideal invariant cross-helicity, $H^\mathrm{C}=\int_S \mathrm{d}S
\mathbf{v}\cdot\mathbf{b}$. The observations are explained by the interplay of
convective driving with the nonlinear spectral transfer of total MHD energy and
cross-helicity.
