Replenishing troops

So I tried a search, and turned up nothing. My question is about how the game decides its going to replenish depleted regiments. I'll pay the money, and leave them in cities and villages or out in the open, and then it seems to be totally random as to when I'll actually get my units fixed up. I've left armies sitting unmoved and unmolested for turns at a time, without ever seeing an extra man. Other times, I'll have paid it and the army is getting attacked time and time again, and then suddenly between battles they'll pick up some replacements up to what I initially paid for. I've even had (rarely) some armies that appear to fix themselves the very next turn whilst on the move, whilst the army sitting in a capital and doing nothing is still waiting for several more turns.

Maybe im not counting turns right, but I see no correlation between location, activity and time on when I can get my casualty replenishments added to an army. What is the mechanic that decides when you'll get all those shiny new soldiers you paid for several turns ago?

It takes two turns for them to receive the replacements. That is all. I know sometimes it seems like 6 or 8 but it is only two turns.

Ships repair by the next turn. Quick and clean.

With armies though, it seems like I never have enough money to repair the whole stack so someone gets left out and it can take a while to get them all fixed up.

2 turns to replenish land units as noted.

The problem is if you hit replenish, the game calculates how many men you are replenishing. If your troops get into combat before those 2 turns finish and lose additional men, they don't get replenished to full strength. They only get replenished precisely by how many men you paid for previously.