Two-dimensional, small-scale forced turbulent flows on the surface of a rotating sphere, along with the familiar Rossby-Haurwitz waves, reveal a new class of waves termed zonons. The zonons form non-dispersive wave packets that propagate in the westward direction with the velocity equal to the phase speed of the most energetic Rossby-Haurwitz wave. Zonons preserve their identity even after the forcing is switched off and the flow undergoes structural reorganization. Zonons reside in locations with the maximum meridional shear and are engaged in strong energy exchange with themean flow. These physical properties of zonons point to their identitywith Rossby solitary waves. The symbiosis between themean flow and the solitarywaves plays an important role in the large-scale dynamics.