Just before the weekend, the National Park Service informed charter boat captains in Florida that the Florida Bay was "closed" due to the shutdown. Until government funding is restored, the fishing boats are prohibited from taking anglers into 1,100 square-miles of open ocean. Fishing is also prohibited at Biscayne National Park during the shutdown.
The Park Service will also have rangers on duty to police the ban. Of access to an ocean. The government will probably use more personnel and spend more resources to attempt to close the ocean, than it would in its normal course of business.
This is governing by temper-tantrum. It is on par with the government's ham-fisted attempts to close the DC WWII Memorial, an open-air public monument that is normally accessible 24 hours a day. By accessible I mean, you walk up to it. When you have finished reflecting, you then walk away from it.