“He did not stumble upon that location,” said the former profiler, Jim Clemente, who retired from the Federal Bureau of Investigation in 2009 as a senior supervisory special agent in the agency’s behavioral analysis unit in Quantico, Va. “He has some familiarity with it.”

Only 4 of the 10 sets of remains have been identified. Those four victims, who were found in December, were all in their 20s and had worked as prostitutes. Each one was reported missing in the summertime — on July 9, 2007; July 12, 2009; June 6, 2010; and Sept. 2, 2010. Investigators have said they believe that the four women were killed shortly after they were reported missing.

The summertime disappearances suggest several characteristics. “There may be a seasonal nature to his connection to the area, or to his fantasy and ritual,” Mr. Clemente said. “It may be the time his wife or kids or parents are away for the summer. There are many possibilities.”

The burlap sacks provide another clue. He could be using them either because they are part of his killing ritual or because they are the easiest cover he can find. Burlap, however, is no longer common, and it might be easier to trace than a plastic bag. “To me, it takes away from his forensic sophistication and criminal sophistication and adds to the possibility that he is more interested in this ritual aspect,” Mr. Clemente said.

Image Joel Rifkin, from East Meadow, N.Y., in 1996. He admitted to killing 17 women between 1989 and 1993, and is now serving a 203-year sentence. Credit... Pool Photo by Neil Schneider

Investigators believe that the deaths of the four prostitutes were the work of a serial killer, but they have not publicly declared a connection between the first four bodies from December and the unidentified ones that were found more recently. The remains of a child may be among those discovered recently, raising the possibility that the dunes may have been used over the years by more than one killer.

The Ocean Parkway serial killer is the third known to have preyed on prostitutes on Long Island in 22 years. Mr. Rifkin, a 34-year-old unemployed gardener from East Meadow, confessed to killing 17 women between 1989 and 1993, when he was arrested. Mr. Shulman, a 42-year-old postal worker from Hicksville, was convicted of killing and dismembering five prostitutes after he was arrested in 1996.