"The last thing I want is my children or anyone's children or any South Australian to be scared of going to the beach," acting South Australian state premier Kevin Foley told local radio on Tuesday in announcing the air patrols.

Foley said he had ordered his children not to go to the beach after 18-year-old surfer Nick Peterson was killed on Thursday by a great white shark, but he would now be happy for his family to venture back into the surf.

Witnesses said a shark up to five metres (16 feet) long attacked Peterson after he fell off a surfboard that friends were towing behind a small boat just offshore.

Australian police and wildlife officers have been ordered to destroy the shark if they catch it, despite a nationwide protection order covering great white sharks.

Foley said up to 80 sharks could be swimming close to Adelaide's beaches at any time, but called for calm and urged people to return to the water, saying there was more chance of a heart attack than being attacked by a shark.

"Let's be realistic about this -- all the air coverage and spotting capacity in the world can't be perfect," Foley told The Australian newspaper.

"We live in dangerous waters."

Australia has a reputation for shark attacks, with three fatal attacks in the past six months, but International Shark File figures show most attacks occur in North American waters.