We introduce a new drift model for slow environmental perturbation affecting modal coupling in optical multi-mode fibers. This model preserves the mode coupling strength asymmetries characteristic to mode pairs of different mode groups while decorrelating the fiber transmission matrix. Existing drift models were derived for the strong coupling regime, in which case the coupling matrix elements are identically distributed, and not suitable for the weak to intermediate coupling regime as shown here. The models' impact on the inherent crosstalk characteristic of a fiber were evaluated for all linear coupling regimes and for fibers with up to 42 spatial and polarization modes. Moreover, transmission performance of 32 GBd 16-QAM (per polarization mode) over the dynamic channel is studied considering singular value decomposition (SVD) pre-coding for the multiple-input multiple-output multi-mode fiber channel. The impact of slow drift on channel equalization performance is evaluated in terms of residual crosstalk. A large discrepancy is observed for fiber channels in the weak and intermediate coupling regimes, while converging in the strong coupling regime. Furthermore, we show that 2 × 1 multiple-input single-output equalizers can be sufficient to compensate for the residual crosstalk in the weak to intermediate linear coupling regime and achieve optimal performance. Index Terms⎯Space-division multiplexing, multi-mode fiber, linear mode coupling, dynamic channel.