Northeast Florida had earlier felt the storm's strong blasts and bands of rain after it came ashore late on Tuesday around Cape Canaveral, forecasters said.
Julia is the 10th named storm and the sixth tropical storm of 2016 in the Atlantic. Isolated rainfall totals of up to 10 inches are possible in some areas.
Other than flood advisories for parts of the SC and Georgia coasts, no tropical watches or warnings were in effect.
"Julia is likely to meander near the northern Georgia and southern SC coastlines into Friday", said National Hurricane Center specialist Richard Pasch.
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At 2 p.m., Julia's eye was spinning 25 miles southeast of Savannah, Ga. and slowly making its way northeast, according to the National Hurricane Center.
The storm was forecast to drop 1 to 3 inches of rain overnight and any heavy rain at high tide in the morning could mean ponding and spot-flooding, according to meteorologist Peter Mohlin of the National Weather Service in Charleston.
Winds are 40 miles per hour, so those will cause some issues, but the big problems will be with rain.
Tropical Storm Julia actually formed over land last night, and is now centered along the coast of Georgia.
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There's a new tropical cyclone in the Atlantic.
Tropical-storm-force winds extend outward up to 45 miles mainly to the northeast and southeast of the center.
A flash flood watch has been issued by the National Weather Service in Wilmington for New Hanover and Brunswick counties due to Tropical Storm Julia.
"We had some pretty good winds associated with it", he said. The hurricane center thinks Julia will weaken to a tropical depression tonight. But as students arrived for classes he said, "so far, everything is a go".
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Tropical Storm Julia, a small weather system parked along the southeastern Atlantic coast, wouldn't be especially noteworthy except for one thing: There's never been another storm like it - at least since record-keeping started.