(CNN) Tropical Storm Dorian is expected to strengthen into a hurricane by Wednesday morning and bring wind, rain and storm surges to the Lesser Antilles and Puerto Rico over the coming week.

tropical storm watch has been issued for Barbados, which means that tropical storm conditions are possible there within about 48 hours.

In addition, watches and warnings for the Windward and Leeward Islands probably will be required later today, and Puerto Rico and Hispaniola should monitor the storm's progress, the National Hurricane Center said.

With maximum sustained winds of almost 40 mph, Dorian is moving west at almost 13 mph. It is expected to continue that way Sunday and then move west-northwest on Monday and Tuesday, the NHC said.

Wind shear and dry air are limiting the storm's ability to organize and strengthen. But as Dorian moves into warmer waters, a weaker wind shear will allow it to strengthen over the coming days.

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