Optimizing bioprocesses requires an in-depth understanding, from a bioengineering perspective, of the cultivation systems used. A bioengineering characterization is typically performed via experimental or numerical methods, which are particularly well-established for stirred bioreactors. For unstirred, non-rigid systems such as wave-mixed bioreactors, numerical methods prove to be problematic, as often only simplified geometries and motions can be assumed. In this work, a general approach for the numerical characterization of non-stirred cultivation systems is demonstrated using the CELL-tainer bioreactor with two degree of freedom motion as an example. In a first step, the motion is recorded via motion capturing, and a 3D model of the culture bag geometry is generated via 3D-scanning. Subsequently, the bioreactor is characterized with respect to mixing time, and oxygen transfer rate, as well as specific power input and temporal Kolmogorov length scale distribution. The results demonstrate that the CELL-tainer with two degrees of freedom outperforms classic wave-mixed bioreactors in terms of oxygen transport. In addition, it was shown that in the cell culture version of the CELL-tainer, the critical Kolmogorov length is not surpassed in any simulation.