NomadPete, we have a very big native pigeon here in NZ, called a kereru. Like most pigeons, there's a lot of noise and flap when they first take off, but also like most pigeons, they go very well once they get going.
During the summer season, they pull a manoeuvre much as you describe: from fast horizontal flight, a tight curved gliding pull up into the vertical , tipping back into a dive just on stall, then a curved gliding pull out. And in steep bush country, I've seen it combined with what topdressing pilots here used to call a split-arsed turn: the pigeon shot out of the bush on a steep hillside, tight curved pull up with a wingover just on stall, down, pull out and shot back into the bush where he came out.
Either way, it's lovely to watch. And they're not bug eaters, so I'm pretty sure it's recreational.
We also have harrier hawks here, they are our only true raptors: they normally soar along hillsides and fencelines at no more than 100-200' looking for lunch. But I've also seen them swooping and rolling up under cloud, and I'm sure they are playing in the turbulence.