Hydromancers are something of a contradiction. They can be as flowing as an Aeromancer, and as forceful as a Geomancer, and switch between the two at the drop of a hat. More importantly, the deeps hold secrets, and many wizards pursue the path of the Hydromancer specifically for the purpose of plumbing them in their search for knowledge and arcane learning.
When you select this archetype at 2nd level, whenever you cast a spell that would forcibly move a creature or knock them prone, they have disadvantage on the saving throw.
Also at 2nd level you gain a swim speed equal to your movement speed. You also add the create or destroy water spell to your spellbook and it counts as a wizard spell for you.
At 6th level whenever you cast a spell that deals force, bludgeoning, acid, or cold damage that requires a saving throw, if the creature fails the save they are either pushed 10 feet away from you or knocked prone, your choice. If the spell instead requires a spell attack roll, you can force the target to make a Strength saving throw against your wizard spell DC or suffer the same. Using this ability on a spell causes the spell to benefit from Inescapable Current. You can do so a number of times equal to your proficiency bonus and regain all expended uses when you finish a long rest.
At 10th Level you are permanently under the effects of a freedom of movement spell. This cannot be dispelled, though it is suppressed by an antimagic field. You can also breath underwater.
At 14th level you gain the ability to ritually cast the commune spell, contacting an entity of the deeps, once per long rest. In addition you can cast commune with nature as a ritual at will, but only in areas with a significant natural body of water (a large river, a swamp, many small rivers, a lake, the coast, at sea, etc.)