  Component-wise dimensionally reduced flows (CWDRFs) are characterized by the
uniformly (over space and time) vanishing of some component(s) in the velocity
gradient tensor, and they may present in various situations with different
conditions. A more universal method for specifying and computing barotropic
CWDRFs associated to the Navier-Stokes equation is designed for situations
besides that in a (cyclic) box. The method is \textit{local} in the sense that
global relations involving volume integration are not used, and the enthalpy
gradient is used as the primitive variable and computed directly. Such a local
method is more useful for, say, testing the physical relevance of CWDRFs,
including the real Schur flows proposed recently, or finding their practically
meaningful realizations. The local and global methods are shown to be
equivalent for CWDRFs in (cyclic) boxes.
