Langmuir turbulence and three-wave nonlinear dynamics

The parametric decay of a single linearly unstable Langmuir wave into broad spectra of damped daughter Langmuir and ion-acoustic waves is studied by means of the Zakharov partial differential equations in one dimension. In the regime investigated, the multimode daughter wave spectra are found to exhibit locked-in-time behavior, allowing a reduction to an equivalent three-mode system. The dynamics of the reduced system are found to be in quantitative agreement with those of the multimode Zakharov simulations. Qualitative agreement is maintained when the ion-acoustic response is reduced from second order to first order. The nonlinear dynamics of the resulting (complex) third-order system are studied analytically and numerically with emphasis on cases when the daughter modes are unequally damped. The special case of exact linear frequency matching between the pump and daughter modes is also considered.