Classic deformation theory includes parameters -- divergence, total strain, and vorticity -- that are invariant to changes in the coordinate system. However, these parameters are sometimes ambiguous with respect to characterizing how fronts are formed and maintained, because the presence of a front imposes a reference coordinate system. To help remedy this ambiguity, we propose a framework in frontal coordinates based on along- and cross-front velocity gradients to better characterize frontal maintenance, which can also be used to define divergence and normal strain in frontal coordinates. The framework with these four parameters defines eight characteristic flow types at a front, providing a complete characterization of the flow that strengthens or weakens a front. This framework higlights the importance of the "strain efficiency" concept, which unambiguously defines the contribution of total strain to frontogenesis. Two examples, one based on a realistic simulation of submesoscales in the northern Gulf of Mexico and the other based on an idealized model with similar flow charactistics, are provided to demonstrate how this framework can be used to enhance our understanding frontal dynamics in submesoscale flows.

front, oceanic submesoscale processes, energy cascade