how to make a Fire waves affect on material with world displacement

Hi, I want to make a cylinder or cube mesh which has waves that resemble the way a fire is burnning

i need it to be in the material itself so i thought of making it using “World displacement” the same way you make waves on a water material

so i looked into some water materials for refrence but every one of them only uses “World displacement” in such a way that the waves basically only going up and down and the affect i want to make is focused on making those waves on the sides rather on the top and bottom of the material

here how the waves of the water material looks like: