The model suggested by the Roman scholar Adrian Goldsworthy is that combat would be broken up by long pauses as each side caught their breath and worked themselves up to enter combat again.
The 'hard' men of that side, be they centurions or huscarls or knights, would advance and drag the men alongside them as they covered the flanks - which would eventually pull the entire formation into close combat. The badasses would be actively fighting, trying to kill their opponents; the other less motivated or more terrified fighters would be fighting defensively, concentrating on not getting hit rather than inflicting wounds.
After a few minutes of this both sides would tire out and if one side didn't break, they'd both pull back to a safe distance and catch their breath and psych themselves up for the next round.