Do field enchantments stack?
Yes; each Drowned Secrets on the battlefield will trigger when the controller casts a blue spell. It is no different than 2 unrelated abilities both triggering upon the same event.

For example, if you had both a Drowned Secrets and a Merrow Levitator on the battlefield and you cast a blue spell, both abilities would trigger. It is no different with 2 separate Drowned Secrets.

Other abilities besides triggered abilities stack as well; such as if you had 2 copies of Honor of the Pure on the battlefield. In that case, White creatures you control would get a total of +2/+2.