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The 893-foot (272 meter) vessel, notorious for reports of raw sewage from overflowing toilets, has been without propulsion and running on emergency generator power since Sunday, when an engine room fire left it adrift in the Gulf of Mexico.
Operated by Carnival Cruise Lines, the flagship brand of global cruise ship giant Carnival Corp , the ship left Galveston, Texas a week ago carrying 3,143 passengers and 1,086 crew. It was supposed to return there on Monday.
Carnival Corp spokesman Vance Gulliksen in Miami said the Triumph was expected to arrive in Mobile later today.
"This is going to be a long day," Terry Thornton, a senior Carnival Cruise Lines vice president, told reporters at the port in Mobile.
He said the ship, which he described as "in excellent shape" after additional provisions were laid in on Wednesday, was near the sea buoy at the entrance to Mobile Bay late on Thursday morning. Getting from the buoy into port normally takes about three hours, Thornton said.
"There is no way we could actually speed up the process to get the ship alongside sooner," he said. "We're making every effort we can to get the ship alongside here in Mobile as quickly as possible."
A Coast Guard cutter has been escorting the Triumph on its long voyage into port since Monday, and a Coast Guard helicopter ferried about 3,000 pounds (1,360 kg) of equipment including a generator to the stricken ship late on Wednesday.
Earlier in the week, some passengers reported on the poor conditions on the Triumph when they contacted relatives and media before their cellphone batteries died.
They said people were getting sick and passengers had been told to use plastic "biohazard" bags as makeshift toilets.
Carnival Cruise Lines President and Chief Executive Gerry Cahill said in a statement late on Wednesday that the company had decided to add further payment of $500 per person to help compensate passengers for "very challenging circumstances" aboard the ship.
"We are very sorry for what our guests have had to endure," Cahill said.
Mary Poret, who spoke to her 12-year-old daughter aboard the Triumph on Monday, rejected Cahill's apology out of hand in comments to CNN on Thursday, as she waited anxiously in Mobile with a friend for the Triumph's arrival.
"Seeing urine and feces sloshing in the halls, sleeping on the floor, nothing to eat, people fighting over food, $500? What's the emotional cost? You can't put money on that," Poret said.
The troubles on the Carnival Triumph occurred a little more than a year after 32 people were killed when the Costa Concordia, a luxury cruise ship operated by Carnival Corp's Costa Cruises brand, was grounded on rocks off the Tuscan island of Giglio in Italy.
Carnival Corp Chairman and CEO Micky Arison faced criticism in January last year for failing to travel to Italy and take personal charge of the Costa Concordia crisis, which unleashed numerous lawsuits against his company.
The cruise ship mogul has taken a low-key approach to the Triumph situation as well, even as it grabbed a growing share of the U.S. media spotlight. His only known public appearance since Sunday was courtside on Tuesday at a game played by his championship Miami Heat basketball team.
Carnival Corp shares were down $0.12 at $37.34 in early afternoon trading on Thursday on the New York Stock Exchange. The shares closed down 4 percent at $37.46 on Wednesday after the company said voyage disruptions and repair costs related to Carnival Triumph could shave up to 10 cents per share off its second-half earnings.
Carnival said it had initially planned to tow the Triumph into Progreso in Mexico, the closest port to its location early on Sunday when the engine room fire occurred. But the ship drifted about 90 nautical miles north, due to strong currents, before the towing got under way, and that left it stranded roughly midway between Progreso and Mobile.