Résumé : We study numerically and experimentally the dynamics of an incoherently pumped passive optical fiber ring cavity nearby the zero-dispersion wavelength of the fiber. We show that the cavity exhibits a quasisoliton turbulence dynamics, whose properties are controlled by the degree of coherence of the injected pump wave: As the coherence of the pump is degraded, the cavity exhibits a transition from the quasisoliton condensation regime toward the weakly nonlinear turbulent regime characterized by short-lived rogue wave events. This behavior is reminiscent of the corresponding dynamics obtained in the purely conservative (Hamiltonian) problem. We report experimental results of an all-integrated incoherently pumped fiber cavity that provide some spectral and temporal complementary signatures of the processes predicted numerically.