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We calculate the evolution of a jet shower due to medium induced splittingsin the deep LPM regime. Due to the characteristic energy dependence of theformation time $t_{\rm form}(\omega)= \sqrt{\omega /\hat{\bar{q}}}$, theradiative break-up process exhibits turbulent characteristics, allowing foranalytic predictions of various inclusive properties of the medium inducedcascade in an inertial range of energies $T \ll \omega \ll E$, where $E$ is theenergy of the jet and $T$ is the temperature of the medium.

Jet fragmentation in a QCD medium: Universal quark/gluon ration and Wave turbulence