Langmuir turbulence as a critical phenomenon. Part 2. Application of the dynamical renormalization group method

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Abstract
In part 1 of this work, we have found a ‘critical curve’ which separates the unstable self-modulation regime from the stable one for a Gibbs ensemble of interacting modes. On this critical curve, the correlation length diverges and scaling invariance occurs; in particular, the Langmuir correlation spectrum is proportional to k-2. Simple laws have been derived for the neighbourhood of the critical curve. However these derivations are based on equilibrium statistical mechanics and the results are obtained with a Hartree approximation which has not been checked. So, in this second part, we elaborate a direct statistical theory of Zakharov's equations completed by excitation sources and dissipations. In spite of infra-red divergences and a large fluctuation level, large-scale properties are derived in the neighbourhood of the critical curve, by the renormalization group method. The laws obtained in part 1 are slightly modified; however, the same spectrum is obtained.