Cyangmou is HELLA right =D.
Here's an excellent vid on it I caught when researching for a fx job I had a little while ago. dont have to watch it all :p
so the outer ring that forms as soon as the object falls is an ejecta sheet , the water column that comes up after the object is submerged is a water jet. fluid dynamics duuude....picked up some lingo after researching. keywords will get ya better results
this one's a comparison of two different scales, the one with the broken up jet is bigger of course.
I made you some GIFs :p
CG, but shows the whole process and is decent enough. maybe a bit too rigid for water, too much surface tension?
these cut before the jet!
however, since you're presumably making this for a game, you have to keep in mind this will play any time the player clashes with the water, so you can skip some detail
Heart of darkness, a game with very detailed fx animation doesnt have an ejecta and a jet, it kinda has a jet that dissipates like an ejecta sheet
some ejecta sheets collapse on the center so it looks like there's no water jet, that's a good simplification
Also, shallow water doesnt create a jet because the jet is proportional to the hole the object leaves behind when submerged. if you only have shallow water in your game you can skip the jet.
So pick a simplification that makes sense with how the player interacts with water in your game grounded on the real phenomena.