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Footage has emerged showing a Norwegian Cruise ship carrying around 4,000 passengers encountering a “bomb cyclone”.

The ship was heading to the Bahamas on a two-week voyage to celebrate the New Year, departing from New York on December 29.

The footage shows the fierce weather conditions that left passengers struggling to walk and caused flooded hallways.

As the ship battled the huge waves and strong winds for three days, some passengers vomited, and many said they felt terrified.

“Sincerely, it sounded as if the boat was just going to break in two,” passenger Brenda Walsh-Matias told WNEP.

“It was the scariest thing I’ve ever experienced. The waves were over 40 feet (12m) and it was continuous — children crying, people seasick, vomiting all over the boat.”

Cruise-goer Christina Mendez told CBS New York of her experience on the ship.

“It was hell for me,” she said. “Water started leaking and then it became so cold we had popsicles inside our room. Flooding [started] in the bathroom because we were at a tilt. The water just gushed out.”

As the situation worsened, passenger Sara Kouri told FOX8 that fear quickly spread amongst the travellers.

“(A woman was) asking me, ‘Are we gonna die?’” Kouri said. “I just kept saying ... ‘We’re gonna be fine,’ and I had no idea if we were gonna be fine.”

Passengers also claimed they were kept in the dark throughout the ordeal, only receiving vague updates from the captain.

“He never told us where we were, how far from New York, how many miles per hour,” Mendez said.

On January 6, the ship returned to New York without any major incidents except the passengers' nightmares from the experience.

Norwegian Cruise Line apologised to guests for the experience and has said the company is talking to individual passengers regarding compensation.

“We sincerely apologize for your discomfort. The weather along the ship's course was stronger than forecasted. All guests and crew are safe and conditions are improving. The ship’s captain will continue to provide frequent updates to all guests. Feel free to DM us for more info,” wrote the cruise line on Twitter.