For my own knowledge, I've been told that a front always lies in a pressure trough. Margules' Frontal Slope Equation and relative minimums and all that. Is this not correct?
I'm pretty sure I've analyzed fronts before that were not coincident with a pressure trough/kink. Anyway, the definition I was taught in school matches what the NWS glossary says:
NWS Glossary said:Front
A boundary or transition zone between two air masses of different density, and thus (usually) of different temperature. A moving front is named according to the advancing air mass, e.g., cold front if colder air is advancing.
The above is also consistent with the AMS Glossary's definition. Their definition does mention that there are several features, including a pressure trough, that commonly accompanies fronts. But I think just the temperature gradient alone suffices to define a front.
I see I'm already arguing about semantics here