Officers, who have stepped up patrols after the attack on Saturday at 7am, need more information to track the attacker down.
DCI Alwyn Bell said: “We have had a number of witnesses and appreciate that. However, there have been people going to work or out jogging and we would appeal to anyone who saw a male running from the Meadows to contact us.”
The man is described as white, aged 20 to 30 years old, around 5ft 4 to 5ft 9 inches tall and of medium build. He was wearing a black beanie-style hat, black zip-up tracksuit top and dark bottoms.
• Faizan Ali, 24, from Edinburgh, has appeared in court charged with the rape of a 28-year-old woman at Leith Links around 1am last Thursday. He made no plea or declaration and was remanded in custody to return to court next week.