  We consider the propagation of temporally incoherent waves in multimode
optical fibers (MMFs) in the framework of the multimode nonlinear Schr\"odinger
(NLS) equation accounting for the impact of the natural structural disorder
that affects light propagation in standard MMFs (random mode coupling and
polarization fluctuations). By averaging the dynamics over the fast disordered
fluctuations, we derive a Manakov equation from the multimode NLS equation,
which reveals that the Raman effect introduces a previously unrecognized
nonlinear coupling among the modes. Applying the wave turbulence theory on the
Manakov equation, we derive a very simple scalar kinetic equation describing
the evolution of the multimode incoherent waves. The structure of the kinetic
equation is analogous to that developed in plasma physics to describe weak
Langmuir turbulence. The extreme simplicity of the derived kinetic equation
provides physical insight into the multimode incoherent wave dynamics. It
reveals the existence of different collective behaviors where all modes
self-consistently form a multimode spectral incoherent soliton state. Such an
incoherent soliton can exhibit a discrete behavior characterized by collective
synchronized spectral oscillations in frequency space. The theory is validated
by accurate numerical simulations: The simulations of the generalized multimode
NLS equation are found in quantitative agreement with those of the derived
scalar kinetic equation without using adjustable parameters.
