The inertial range spectrum for a caviton model of Langmuir turbulence

We calculate the spectral index for the Langmuir turbulence spectrum, assuming that the bulk of the energy is contained within a set of strongly flattened, non-interacting cavitons which are subject to supersonic collapse, which preserves the plasmon number in the caviton, as well as an intability, also plasmon conserving, causing splitting. The spectral index, which in the absence of splitting is $\text{-5}\text{2}$, increases when there is splitting, corresponding to a considerable flattening of the spectrum in the inertial range; if the splitting leads to two new cavitons, the resulting index is -1.73.