The day after Tiger Woods and Lindsey Vonn posted formal, studio-quality photographs on their Facebook and Twitter accounts to show that they are dating, tennis star Caroline Wozniacki posted her own sports power-couple shot on Twitter.

In Wozniacki’s photo, taken at a players’ party a night before the start of the Sony Open in Miami, Wozniacki stuffed her blond hair, which falls past her shoulders, under a black Harpo Marx wig and stood next to her boyfriend, the clown-haired golf star Rory McIlroy. They pointed at each other as if to say, “I’m with Curly.”

Wozniacki and McIlroy are not a tightly wound pair. They are openly affectionate, conducting their romance as if they were huddled over a table in a crowded diner and not on display like celebrities in captivity.

Through the ordinariness of their relationship, Wozniacki and McIlroy enjoy the privacy that Woods and Vonn pointedly asked for, the right to exist, in Woods’ words, “as an ordinary couple.”

At the Honda Classic in Florida, McIlroy talked about loading the iPod he gave Wozniacki last year for Christmas with ballads from the boy bands that she loves and he has learned to tolerate. At a Masters Series event in California two weeks later, Wozniacki ticked off a list of obligations, including a charity golf event and a photo shoot, that prevented McIlroy, the top-ranked men’s golfer, from travelling to watch her play.
When he became ill from the heat during a tournament last year in the Middle East, McIlroy spoke of how Wozniacki, who had accompanied him, nursed him back to health with a lemon-juice concoction.

By not disguising their relationship, Wozniacki, 22, and McIlroy, 23, have given it a cover of normalcy, which Wozniacki views as having helped them. “I think people are very respectful when we want to come out and support the other,” she said. “They don’t want to disturb us.”

The two met in July 2011 at a heavyweight fight in Germany, their ringside seats attesting to their status. Wozniacki was the top-ranked women’s tennis player and in the midst of a six-win season. McIlroy had won his first PGA Tour event a few months earlier and was ranked No 4.

A boy from Northern Ireland and a girl from Denmark, they instantly found common ground. As sports prodigies, they were being interviewed on national TV at age 9, had turned pro as teenagers and remained close to their parents. They have each earned more than $15 million in prize money and appearance fees.

In an interview last year for the BBC documentary “Rory: Being Number One,” Wozniacki said: “For me, I think it’s great that we both have our own careers so not one is just waiting at home for the other one. I know what he’s going through. When he plays amazing, I know how he feels, and also, when he’s going through a rough path, how that feels and how to handle the situation.”

After winning five PGA Tour events in 2012, McIlroy stumbled out of the gate this year. He missed the cut in his opener in Abu Dhabi in the United Arab Emirates; lost in the first round of his next event, a match-play event outside Tucson; and withdrew with a sore wisdom tooth midway through the second round of his third start.

If anybody possessed the vocabulary to talk him out of the abyss, it was Wozniacki, who won four fewer titles last year than the six she collected in 2011 and lost her No 1 ranking.

McIlroy’s  ascension to the top spot was aided by his much-improved fitness, for which he credits Wozniacki. In an interview this month, he said he considered himself in good shape until he joined Wozniacki on one of her daily 45-minute runs near her home in Monte Carlo.

“I struggled a bit,” he said.

In a separate interview, Wozniacki ran with the narrative. “He didn’t make it,” she said.
With a twinkle in her eyes, she described his determination to keep up.
“The improvement I have seen with his fitness is unbelievable,” Wozniacki said, adding: “He’s going to the gym at least once or twice a day, and I think he loves it. He loves it more than me, and I like to go to the gym.”

During her brief off-season, Wozniacki wondered whether she had created a workout monster. McIlroy kept pestering her to join him in the gym, she said, until she told him: “Can you just rest for a second? I don’t want to see the gym. I don’t want to hear about the gym. I don’t want to go run. I just want to relax.”'

She added: “But it’s good fun. It’s great that we can motivate each other. It’s great that we can do so many things together. That just makes it a lot of fun.”
McIlroy’s aggressive play, which keyed his eight-stroke victories at the 2011 US Open and the 2012 PGA Championship, has rubbed off, if only slightly, on Wozniacki, who wins points with her dogged defense.

“I’ve been working on my net game a lot and my volleys,” said Wozniacki, the queen of the 20-stroke rally, “and my volleys have definitely improved.”

She and McIlroy are good-natured about ceding the spotlight to the other. McIlroy acknowledged that Jack Nicklaus, who has become an avid tennis player since retiring from tournament golf, had asked him if he thought Wozniacki would be interested in joining him for a match. Laughing, McIlroy said: “I told him, ‘What about me? Don’t you want to play golf with me?”'

That led Wozniacki to say that while attending a Formula One race in Abu Dhabi with McIlroy, she spotted the soccer star Ronaldo and excitedly pointed him out. The next thing she knew, she said, Ronaldo approached them. He introduced himself to McIlroy, she said, hugged him and informed him that he was a big fan of golf. Laughing, Wozniacki said: “I was like, ‘What about me? Don’t you like tennis?”'

McIlroy risked displeasing one of the golfing greats when he bypassed Arnold Palmer’s tournament this weekend to be with Wozniacki, whom he had not seen, except for their hourlong Skype talks, in more than a month. On Thursday he waded through the crowd to get to his seat between his parents at Crandon Park Tennis Center’s Grandstand court in Miami.

Under a broiling mid-afternoon sun, Wozniacki outlasted Karolina Pliskova in three sets. McIlroy ducked out with his parents immediately after the match. Two hours later, Wozniacki left with her parents.

The next day, McIlroy joined Wozniacki on a three-mile run. He later showed up at the practice courts for the final 15 minutes of her one-hour hitting session, which her father conducted while her mother watched.

At the sight of McIlroy, a murmur went through the crowd of spectators who had gathered along the fence.

One mother pointed out McIlroy to her daughter, who was hugging an oversize tennis ball, and said: “Her boyfriend’s with her. He’s the golfer. Get his signature. His name’s even bigger.”