We present a pair of coupled equations that shows the nonlinear coupling between a newly discovered low-frequency dispersive electromagnetic mode and flute-like electrostatic convective cells in a non-uniform dusty magnetoplasma. From the coupled mode equations we obtain a nonlinear dispersion relation, which predicts efficient excitation of convective cells at the expense of the dispersive electromagnetic wave energy. The relevance of our investigation to the transfer of energy from short-scale electromagnetic waves to long-scale convective cells in tokamak plasmas is pointed out.