Tropical Storm Chantal, the third named storm of the 2013 Atlantic hurricane season, barreled through the Leeward Islands and into the Caribbean Sea Tuesday, following a projected path that will take the fast-moving cyclone over Hispaniola Wednesday evening and up through the Bahamas toward the U.S. mainland by this weekend.

According to the 8 p.m. AST alert from the National Hurricane Center in Miami, Chantal was located about 220 miles south-southeast of San Juan, Puerto Rico, or about 395 miles east-southeast of Santo Domingo, Dominican Republic, moving west-northwest at 26 mph. The relatively small storm packed near hurricane-force winds of 65 mph that extended outward up to 90 miles north of the center.

Tropical storm watches Tuesday evening stretched from the Virgin Islands up through the central Bahamas, while Puerto Rico, the island of Hispaniola, the Turks and Caicos, and the southeastern Bahamas all remained under tropical storm warnings. A hurricane watch, meanwhile, was in effect for the eastern coast of the Dominican Republic from Samana to Barahona.

The National Hurricane Center said tropical storm conditions would likely reach Puerto Rico overnight Tuesday and spread into the Dominican Republic by Wednesday morning. Both islands could see heavy rains, dangerous storm surges and water levels up by as much as 4 feet.

Accuweather Senior Meteorologist Alex Sosnowski said the greatest threat would be from flooding over Puerto Rico and Hispaniola. “While fast movement of Chantal will limit the amount of rain on the smaller islands, large mountains of the Greater Antilles will squeeze out tremendous moisture, regardless of the forward speed of the storm.”

The menacing storm has already caused numerous travel disruptions, and more are likely to come.

LIAT, “The Caribbean Airline,” canceled more than a dozen flights due to airport closures in the Lesser Antilles, including four flights scheduled for Thursday. A spokesperson said customers affected by the disruptions could change flights for free within one week of the date of their original scheduled travel.

JetBlue offered fee waivers for those booked on flights to Barbados and St. Lucia Tuesday who needed to change their dates. The low-cost carrier extended the offer to anyone booked on flights to or from Puerto Rico or the Dominican Republic Wednesday.

Given the large population of Dominicans and Puerto Ricans in the U.S. and the popularity of those two islands with vacationers, numerous other airlines have issued travel alerts for the next two days.

United Airlines will allow travelers headed to Puerto Rico or the Dominican Republic Wednesday to change for another date through July 13. All fees and fare differences will be waived.

American Airlines, which operates several trips to the Caribbean on its American Eagle affiliate, has asked travelers flying to the Dominican Republic, Haiti and Puerto Rico Wednesday to travel on Thursday instead at no additional cost.

US Airways will allow anyone booked for travel to the Dominican Republic or Turks and Caicos Islands Wednesday or Thursday to change their dates fee-free for travel through July 14.

Cruises, meanwhile, have a different modus operandi when storms like Chantal threaten their itineraries. They rarely cancel trips, choosing instead to re-route to destinations away from oncoming cyclones.

Carnival Cruise Lines has altered the itineraries of the 2,974-passenger Carnival Liberty and the 2,758-passenger Carnival Victory. The Liberty skipped a visit to St. Thomas in the U.S. Virgin Islands Tuesday, and instead stopped in San Juan a day earlier than scheduled. It will also stop in Grand Turk a day ahead of schedule Wednesday and then head to Nassau in the Bahamas on Friday. The Victory, meanwhile, also flopped its scheduled stops around to accommodate the storm and added a call in Nassau.

If Tropical Storm Chantal follows along its projected path along the Florida coast, cruises departing from Miami up through Port Canaveral, Fla., could also be affected in the coming days.