what was the function of the Roman cavalry?

[L C Cinna]

Well I can just point at the 2 accounts from Iosephus again I posted on page 1. Imho it describes the actions of Roman cavalry against loose "formations" very well.

Close order trained infantry is another question. but if you imagine you are engaged with some legionaries in front of you and you have an ala of approx 500 horse coming in from the flanks throwing javelins at you constantly while being too fast for you to do anything against them.

I guess some 2000 javelins thrown at you will seriously disrupt coherence of a formation or at least force some people to turn and face towards the cavalry to protect the rest with their shields. This will cause your formation to lose it's forward pressure and makes it easier for the legionaries to break it. So whether the javelins will break the formation or the infantry from the front will do so after the unit was disturbed by the javelins. Now the cavalry can draw swords and rush in.