The latest guidance suggests that the strongest winds will occur along the south and west coasts, where gusts could exceed 130-140 kph.
There are no coastal watches or warnings in effect.
Isaac was a hurricane Sunday night but downgraded when maximum sustained winds fell below 74 miles per hour.
The turbulent weather is coming off the back of one of number of major storms now raging in the Atlantic, another of which, Hurricane Florence, has caused mass evacuations on the east coast of United States this week.
At 1100 a.m. AST (1500 UTC), the center of Subtropical Storm Joyce was located near latitude 33.7 north, longitude 43.7 west.
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The Miami-based National Hurricane Centre (NHC) in its latest bulletin said that hurricane watches had gone into effect for Dominica, Martinique, and Guadeloupe, while a tropical storm watch is in effect for Antigua and Barbuda and Montserrat.
"In a couple of days, while the wind shear could decrease over the east-central Caribbean Sea, there might not be much of a system left to take advantage of the more conducive conditions". The hurricane center is giving the system a 50 percent chance of becoming a tropical depression or storm within the next five days.
"At this time, Tropical Storm Isaac is not considered an imminent threat to the Cayman Islands but that could change", said Tara Rivers, Minister responsible for HMCI.
It's not clear if the storm is expected to strengthen back into a hurricane after it hits the eastern Caribbean.
Two high pressure ridges are still expected to be strong enough to force Florence to stall just before, or after, it makes landfall somewhere near the North Carolina/South Carolina border early Friday.
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The National Hurricane Center says Hurricane Florence is expected to bring life-threatening storm surge and rainfall to portions of the Carolinas and mid-Atlantic states. Earlier forecasts showed that the storm was slated to directly hit around North and SC.
Over in the Pacific, this storm is still moving toward Hawaii, where tropical storm warnings and watches have been issued, the hurricane center said.
The storm is likely to die out by Wednesday, the forecaster said. The storm is moving toward the west-southwest near 6 miles per hour (9 km/h). Sustained winds slowed slightly to 125 miles per hour Tuesday afternoon, making it a Cat 3 storm.
Meteorologists are also keeping an eye on yet another tropical disturbance that's spinning in the western Gulf of Mexico. "Intermittent rain bands are expected on St. Croix as Isaac passes south of the big island".
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