Broughty Ferry Councillor Charles Webster said the time has now come to license these craft, which are capable of travelling at 80mph.

David Kett said, “These injuries could be due to a straightforward accident, or aggression from other sea creatures, although increasingly it is feared they might have been caught unawares by high-speed craft crossing their path,” he said.

Mark Simmonds, director of the Whale and Dolphin Conservation Society, said, typically, damage to the dorsal fins or the back is the result of being struck by a water vehicle.

MVS Tay Unit operates vessels from both sides of the Tay taking passengers on tours of the estuary and dolphin-spotting trips.

“The guidelines for all craft except ships on passage is to slow down or stop at some distance from the pod, don’t make any sudden engine manoeuvres, and let the dolphins come to you,” said Mr Kett.

Councillor Webster said, “I’m distressed to learn about these horrific injuries. If they are due to fighting amongst dolphins, there’s not a lot we can do about it.

“If however they are due to fast-moving craft in the water then obviously we have to take action.

“The time has now come to license the use of these crafts. I’m not for restricting freedom, but there comes a time when use has to be confined to licensed users, as they do with motorcycles and vehicles on the road.

“I’m sure most responsible users wouldn’t have a problem with that.

“Having witnessed the irresponsible behaviour of a small minority of jet-skiers, there should be no room on the water for these people.

“There have been some spectacular displays from the dolphins, much to the enjoyment of people watching at Broughty Ferry. We don’t want to drive them away.”

The dolphins started to arrive several years ago, their presence mirrored by decreasing numbers in the Moray Firth. It is thought pollution and noise from rising numbers of dolphin-watching tourist boats drove them from their habitat there and other east coast areas.

Mark Simmonds said, “Jet-skis and dolphins don’t mix. Whales and dolphins are air breathers and cannot simply dive away under the water and hide and they may not be able to outpace or out-manoeuvre fast vessels.

“So we are asking boat users please not to chase them and to be careful when manoeuvring if these animals are nearby.”

Dundee City Council is working in conjunction with Tayjet Personal Waterfront Club, which represents responsible jet-skiers, to try to ensure the safety of the dolphins.

Councillor Charles Farquhar, leisure & arts convener, Dundee City Council said, “It would be extremely sad if dolphins had been injured in any way by fast craft using the River Tay.

“This shows why the council’s earlier warning to irresponsible jet-ski users needs to be reinforced. We will be continuing to work with Tayjet Personal Waterfront Club, who represent responsible enthusiasts who use the water safely, the port authority, Tayside Police and other agencies, to deal with the problem.

“The dolphins are a magnificent sight in the water and are becoming a popular attraction that is bringing people to Dundee from far and wide. We must not let reckless people threaten this real wildlife treasure of the River Tay.”