With the eye of Florence stalled near the coast, the half of the storm still out over the Atlantic continued to collect warm ocean water and dump it on land.
Winds of 40 mph extend outward up to 115 miles (185 km) from the center of the tropical cyclone.
A small-craft warning means in this case that surface winds greater than or equal to 25 knots and seas equal to or greater than 3 metres (10ft) are already affecting or expected to affect the marine area.
The National Hurricane Center said Florence will eventually break up over the southern Appalachians and make a right hook to the northeast, its rainy remnants moving into the mid-Atlantic states and New England by the middle of next week.
The public are warned that road, rail, air, and ferry services are likely to be affected, with longer journey times and cancellations a possibility.
Isaac's death knell was sounded around 5 a.m. Saturday when the National Hurricane Center's aircraft was unable to find a well-defined center and as a result the center reported that the storm had "dissipated".
Olivia's maximum sustained winds are about 60 miles per hour, after the storm weakened from Category 1 strength, forecasters said.
Tropical Storm Isaac made its closest approach to St. Croix Thursday night, passing nearly 200 miles to the south and having no apparent impact on the territory as it made its leisurely way across the Caribbean.
Forecasters warned that drenching rains of anywhere from 1 to 3½ feet as the storm crawls westward across North and SC could trigger epic flooding well inland over the next few days. Gusts of wind expected will be around 55-65 miles per hour (88-104 km/h).
"These enormous waves are produced by being trapped along with very strong winds moving in the same direction (as) the storm's motion", explained a tweet sent by the analysis branch.
An additional three feet of water would bring the storm surge to 6 feet high, potentially destroying homes along the coastline.
On that path Isaac will move across the central Lesser Antilles and into the Caribbean on Thursday.
The NHC said Helene could bring up to 4 inches of rain to the Azores and isolated amounts up to 8 inches, as well as life-threatening surf and rip current conditions.
"Interests elsewhere in the southeastern and mid-Atlantic states should monitor the progress of Florence", said the NHC.