  Mode-based model-reduction is used to reduce the degrees of freedom of high
dimensional systems, often by describing the system state by a linear
combination of spatial modes. Transport dominated phenomena, ubiquitous in
technical and scientific applications, often require a large number of linear
modes to obtain a small representation error. This difficulty, even for the
most simple transports, originates from the inappropriateness of the
decomposition structure in time dependent amplitudes of purely spatial modes.
  In this article an approach is discussed, which decomposes a flow field into
several fields of co-moving frames, where each one can be approximated by a few
modes. The method of decomposition is formulated as an optimization problem.
Different singular-value-based objective functions are discussed and connected
to former formulations. A boundary treatment is provided. The decomposition is
applied to generic cases and to a technically relevant flow configuration of
combustion physics.
