Rob Taylor, who weighs 290 and has forearms like footballs, is Batman. Rick Kenyon, begrudgingly, is Robin, though he's the one who drives the cruiser.
The officers know almost everyone in the park, including the four just caught drinking beer. They've worked downtown together for about six years.
They have offered help to nearly every homeless person here. But shelters come with rules, and most require sobriety.
The synthetic drugs have made the cops' jobs even harder.
Florida has banned many of the common ingredients, but manufacturers continually adjust the formula.
"This spice is unbelievable," Kenyon says. "We've had some guys for 10 years and we've never had a problem with them. Now, the same guys are on this spice and they want to fight us."
The officers say they're fair, but give no breaks. The work is unrelenting.
Between early 2008 and 2012, there were 2,739 arrests made in the park. That's an average of about two per day.
The police presence, many argue, treats the park's symptoms but not its essential problems.
Mayor Bill Foster believes programs such as concerts and markets eventually will make the lawbreakers too uncomfortable to stay.
But public and private interests have for years tried to fix it: fresh gardens and street lamps, a refurbished bandstand and bathrooms, fewer benches, a nighttime closure and new neighboring businesses
At 11:30 a.m., Terolli is lounging by the fountain.
In Connecticut, at age 19, he got a job working with hazardous materials that paid $1,400 a week, more money than he could handle. Heroin hooked him.
"I came down here," he says, "to get clean."
He was in a car accident about a year ago. He got a doctor to prescribe pain pills for back pain he didn't have. He blew a $50,000 settlement on drugs and booze.
He comes to Williams Park to feed his habits. To eat and sometimes get a hotel, he sells the pills he doesn't take.
"Unless you're a drunk, a drug addict or a druggie," Terolli says, "you don't want to be here."
He stands up.
"You want me to give you an example? Count to 20."
He approaches a man on a nearby bench where many of the park's elicit drugs are purchased.
With five seconds to spare, he returns. He spins a joint in his fingers.
"PCP," he says. "Angel dust."
He takes a drag. His eyelids sag, his words crash together.
He smokes the joint until it's the size of a jelly bean. He flicks it onto the concrete path.
A thin-faced man with sunken eyes darts over and picks it up. He puts it to his lips and inhales.
By 1:45 p.m., the drugs and alcohol are in full effect. The morning's bustle has waned. People nap beneath the trees.
Larry Fultz sells hot dogs on the northwest corner. After four years, he has perfected the art of "no": to requests for sodas, cigarettes and, of course, hot dogs.
The palm frond artists have made $20. Wilson buys 305's cigars and Nutty Bars. Then back to his refrain: "Buy a rose for the special someone that you love?"
Near the bandstand, "Pops" has arrived. Robert Butler has sat on the same bench almost every day for the past 15 years. He won't reveal his age, but time has turned his beard white.
He gazes at the bandstand and imagines the music he heard ring from its stage as a boy.
He leans on a wooden cane and, in a plodding Southern accent, dispenses wisdom.
Butler sits with his back to the drug dealers: "Ain't nothin' but problems back that way."
By 4:50 p.m., the park has thinned. The Batmobile is parked on the grass near the southwest corner. Taylor and Kenyon patrol from 4 to 6 p.m. as commuters get on and off the buses. The smoke is so oppressive that it gives passers-by headaches.
The drug bench is empty, but not all the transactions are done.
A hustler, who is drunk, sets a pair of black Nike sneakers on the memorial wall.
"Two dollars," he says to his target, a man on a bike.
"They ain't got no shoelaces," the biker says. Plus, he only has a buck.
The hustler calls it a deal. The biker rides away with the shoes.
"I'm fixin' to do what I got to do," says the hustler, grinning. He stumbles across the road, in search of the day's eighth beer.
By 6:15 p.m., the Batmobile is gone. The park's residents trickle back as lights stringed around the oaks switch on.
On First Avenue N, an ambulance pulls between the buses.
Troy "Happy" Gilmore sits on the wall, teetering. He stares at the ground. He takes deep breaths. He is 35, a recovering crack cocaine addict. He has been arrested 55 times since 2005.
"Pneumonia," says his boyfriend, Timothy Barker. "He can't breathe."
A paramedic approaches.
"On that spice crap again?" he says. "That's what it was last time."
Gilmore climbs into the ambulance.
"He's a regular," the paramedic says before they pull away.
It's just past 7 p.m. The park doesn't close for four more hours, but the sun has faded along with most of the daytime inhabitants.
Two new officers begin night patrol. They catch a man rolling spice joints in a bus shelter. They confiscate the drugs and take his information. If the lab shows it contains a banned substance, they'll come back to arrest him.
The southwest corner is littered, with cigarette butts, discarded spice pouches, an empty ramen cup. The area is deserted but for a man with a curly red beard who has collapsed in the bushes.
The officers hoist him up and onto a bench. He must leave, they explain, or he'll be taken away. He slumps over, revealing the text on his shirt: "Alcatraz Psycho Ward Outpatient."
The man sits for a while, then stands. He totters north up the sidewalk, past flickering police lights and beeping buses and squirrels collecting the day's leftovers. He collapses, but gets back up. He reaches a bus shelter and stops to rest. At last, he rises.
He crosses the road and ambles into the darkness, leaving Williams Park to its rest.
Times researcher Caryn Baird and photographer Will Vragovic contributed to this report.