The two-field equations that govern fully nonlinear dynamics of the drift wave (DW) and geodesic acoustic mode (GAM) interaction in toroidal geometry are derived within the nonlinear gyrokinetic framework. Two stages with distinctive features are identified and analyzed using both analytical and numerical approaches. In the 'linear' growth stage, the derived set of nonlinear equations can be reduced to the intensively studied parametric decay instability, accounting for the spontaneous resonant excitation of GAM by the DW. The main results of previous works on spontaneous GAM excitation, e.g. the greatly enhanced GAM group velocity and the nonlinear growth rate of GAM, are reproduced from the numerical solution of the two-field equations. In the fully nonlinear stage, soliton structures are observed to form due to the balancing of the self-trapping effect by the spontaneously excited GAM and kinetic dispersiveness of the DW. The soliton structures enhance turbulence spreading from the DW linearly unstable region to the stable region, exhibiting convective propagation instead of a typical linear dispersive process, and are thus expected to induce core-edge interaction and nonlocal transport.
Zonal flows induced by symmetry breaking with existence of geodesic acoustic modes