The mouth of the Irvine (pronounced Ir-vin not Ir-vyne as it is mangled in Australia) runs between Irvine town and Fularton into the Firth of Clyde. From here it runs roughly east passing between Kilmarnock and Riccarton then Galston, Newmilns and Darvel.
Ayrshire is divided into four districts (from the north)
Cuninghame
Kyle Stewart
King's Kyle
Carrick
Carrick was formerly the northern limit of Galloway influence but was taken and given to staunch supporters of the crown as a barrier to the wild Galwegians.
Cuninghame (King's Home) borders on Renfrew
Kyle in the middle was divided into Kyle Stewart which was under Stewart influence and King's Kyle which was retained by the king (before the Stewarts)with its barons directly appointed by the king for their loyalty and ability to also stand fast against the horrible Galwegians.
The border between Kyle Stewart and Cunninghame is the Irvine River itself.
Between Kyle Stewart and King's Kyle the River Ayr.
Between King's Kyle and Carrick the River Doon.
The early Galwegians were (I think) considered fiercer and ruder than even the highlanders. They might even have been the almost legendary Attacotti raiders separately named and feared by the Romans. Things improved eventually (must have as I have Galwegian ancestors as well).
I will upload a map to my new site with nothing in it once I figure out how.