In 1988, the U.S. Ohio-class submarine USS Montana has an encounter with an unidentified submerged object and sinks near the Cayman Trough. With Soviet ships moving in to try to salvage the sub and a hurricane moving over the area, the U.S. government opts to send a SEAL team to Deep Core, a privately-owned experimental underwater drilling platform near the Cayman Trough to use as a base of operations. The platform's designer, Dr. Lindsey Brigman, insists on coming along with the SEAL team, despite her estranged husband Virgil "Bud" Brigman being the current foreman.
During initial investigation of the Montana, a power outage in the team's submersibles leads to Lindsey seeing a strange light circling the sub. At the same time, one of Deep Core's crew, "Jammer", damages his breathing apparatus in an apparent panic, and falls into a coma. This prompts the admiral in charge of the operation to send Lt. Coffey, the SEAL team leader, to take one of the mini-subs and recover a Trident missile warhead from the Montana, just as the storm hits above. Coffey does not get permission from the Deep Core crew. The Benthic Explorer, which Deep Core is tethered to, is rocked by the storm, and the cable crane is torn from the ship. The crane falls into the trench and, without the mini-sub to disconnect the cable, Deep Core is dragged towards the trench, stopping just short of it. The rig is partially flooded, killing several crew members and damaging its power systems. Coffey shows little remorse when he and his SEALs return to the damaged base.
Lindsey is sent in dive gear to retrieve some oxygen bottles from a damaged portion of the rig to give the crew enough time to wait out the storm. While working, she's accosted by a small, maneuverable pink/purple device, followed by a much larger one. Before she can take a picture as proof, the large craft zooms downward into the trench, leaving her to take fuzzy, smeared pictures of the smaller one following it. She coins the term "non-terrestrial intelligence", or "NTI". As the crew struggles against the cold, they find an NTI has formed a living column of water and is exploring the base. Though they treat it with curiosity, Coffey is agitated by it and cuts it in half by closing a pressure bulkhead on it, causing it to retreat. The crew becomes convinced that Coffey is suffering paranoia from high-pressure nervous syndrome. Spying on him through a remote operated vehicle, they find he and another SEAL are arming the warhead to attack the NTIs, and race to stop him. Bud fights Coffey but Coffey escapes in a mini-sub with the primed warhead, and Bud and Lindsay give chase in the other sub. Coffey is able to launch the warhead into the trench, but his sub is damaged and drifts over the edge of the trough, and he is crushed when the sub implodes from high pressures. The other mini-sub is also damaged and is taking on water; with only one functional diving suit, Lindsay opts to enter deep hibernation when the ocean's cold water engulfs her, and Bud swims back with her body to the platform. There, he and the crew administer CPR and revive her. Bud and Lindsay reaffirm their lost love.
One SEAL, unaware of Coffey's plan at the time, helps to locate the warhead, stopped on a ledge several thousand feet down the trench. Bud volunteers to use an experimental diving suit equipped with a liquid breathing apparatus to survive to that depth, though he will only be able to communicate through a keypad on the suit. Bud begins his dive, assisted by Lindsay's voice keeping him coherent against the effects of the mounting pressure, and reaches the warhead. The SEAL guides him in disarming it, but his only light source is yellow, making two high-contrast striped wires appear identical, forcing him to make a 50-50 choice on which wire to cut. With nearly no oxygen left in the system, Bud types out that he knew this was a one-way trip, and tells Lindsay he loves her. As he waits for death, an NTI approaches Bud and takes his hand. He is guided to an alien ship deeper in the trench. Deep inside, the NTI creates an atmospheric pocket for Bud, allowing him to breathe normally. The NTI plays back Bud's message to his wife and the two look at each other with understanding.
On Deep Core the crew is waiting for rescue when they see a message from Bud that he met some friends and warning them to hold on. The base shakes and lights from the trench bring the arrival of the alien ship. It rises to the ocean's surface, with Deep Core and several of the surface ships run aground on its hull. The crew of Deep Core leave the platform, surprised they aren't suffering from decompression sickness, when they see Bud walking out of the alien ship. Lindsay races to hug Bud.

Question: What does the power outage in the SEAL teams submarine lead Dr. Lindsey to see?
Answer: A strange light circling the submarine. 
Alternative answer: A strange light circling the sub.