Splashing in an indoor swimming pool in Manhattan, a group of young men and women tried to keep their heads under water for more than a few moments before they came back up for air. Some of them had already acquired the skills to shoot down rockets and operate tanks while serving as American soldiers in the Middle East. Now they were learning to swim.

Hopping into the pool to join them, an exuberant septuagenarian in a blue swimsuit bellowed orders at her charges, a mix of veterans and students at John Jay College of Criminal Justice. Some were learning to swim for the first time, while others were there to perfect their techniques or for therapeutic or rehabilitative reasons.

“Who are we?” she asked.

“WETs 4 Vets,” the swimmers replied in unison, military style, as they treaded water in an ever-expanding circle. Then they started chanting “John Jay” in syncopated staccato, laughing as they grew more comfortable in the water. American flags protruded from their caps like feathers from a fedora. (WET stands for water exercise techniques).

“Buddy up with one person, we’re going to do our relay,” their teacher, Jane Katz, instructed. “Everyone say hello to your new buddy. And leave some water in the pool.”

Veterans and civilians paired up holding kickboards, high-fiving.

Jonathan Martinez, 27, had recently graduated from the 10-week program and was now helping teach his fellow veterans. After growing up in the Bushwick section of Brooklyn, he served in the Army from 2008 to 2013 in eastern Afghanistan. On an operation against the Taliban two weeks before he was due to leave, he was hit by a shell and fell from a cliff, fracturing a vertebra and paralyzing the left side of his body. He spent a year in rehab and connected with Jane through her program.

“We started doing physical therapy in the water, and I realized swimming would help me,” he said. “I joined two years ago, and I never left.”

Now he is fully ambulatory again and a swimming-as-physical-therapy convert.

“Don’t be too confident and think you’re the most baddest one in the water,” he advised the students in the pool. “You have to learn the technique, what Dr. Katz is teaching you guys.”

Dr. Katz, 74, a professor of health and physical education and emeritus head coach of women’s swimming at John Jay, started teaching veterans to swim in 2012 because she felt it could be a critical part of their rehabilitation. She competed in the 1964 Olympics in Tokyo with the synchronized swimming performance team, and she has basically kept the same pace in the water ever since. She competed in the Senior Games in June. Dr. Katz has used swimming to help with her own recoveries, after being hit by a car in 1961 and rammed by a drunken driver after that. She has a particular eagerness to help veterans.

“My father was a veteran, and my husband was a veteran,” she said. “Veterans are critical to this nation, and swimming is not only an essential skill; it can help them in recovery. And in this program, we bring civilians to meet the veterans, which helps them move back into society too.”

Dr. Katz said for many of her students, even if they were vaguely familiar with swimming before, the class helped them refine their proficiency, teaching them an essential skill and building their confidence. Of Mr. Martinez, she said, “When I met him, he was doing what I call the ‘Coney Island East River Crawl,’ with his head sticking out of the water as he paddled for dear life.”

Now, Mr. Martinez is proficient in several different strokes and has become Dr. Katz’s assistant teacher.

Standing at the side of the pool, Dr. Katz looked out at the diverse group of swimmers with varying configurations of scars and military tattoos as they bounced a beach ball around the shallow end, the flags sticking upright from their caps.

Then she told them to put their face in the water and make bubbles.

Saaif Alam, 20, who grew up in Jamaica, Queens, was not a veteran but joined the program as a student to learn to become a stronger swimmer. As he stood beside the pool, his pale yellow swim trunks clung to his thin frame.

“My father told me he learned to swim in a deep river in Bangladesh, but we didn’t have that in Queens,” he said. “I would practice at the Y.M.C.A., but I couldn’t figure out how to breathe underwater. It took me two weeks to learn here. Maybe next I’ll go in the deep end.”

Dr. Katz looked on and agreed.

“Of course he can do it,” she said. “They’re all determined. I tell them they can always be better.”