Hydrilla, the prolific American strain of a pesky underwater Asian plant, is now firmly rooted along a 12-mile stretch of the Potomac River between Alexandria and Mount Vernon, according to a study by federal and local scientists.

And the shoreline survey reveals that stands of hydrilla have tripled in size since June along that area. The study also produced some good news: that the plant has not spread farther along the river since its discovery here last year.

The blooming of hydrilla along the shores of the Potomac has divided scientists, said William Anderson, chief regional scientist for the National Park Service, one of half a dozen governmental agencies engaged in the study. Some scientists want to control it through the use of herbicides, and others oppose that step, Anderson said.

A major problem confronting any eradication program is that hydrilla can survive in the upper Potomac, where virtually no submerged plants have lived for almost 50 years because of pollution.

The U.S. Geological Survey a year ago issued a Potomac River report hailing the return of underwater plant life as "a significant indicator of the health" of the river and a boon for fish and fishermen, since fish and wildlife feed on the plants. That was before some of hydrilla's problems were known.

Thick mats of hydrilla this summer created an almost impenetrable Sargasso Sea around Dyke Marsh and the Belle Haven Marina south of Alexandria. Hydrilla was accidentally planted there several years ago, apparently by a Park Service scientist.

The water weed, which affects both motorboats and sailboats, is on the Army Corps of Engineers list of "nuisance" plants that impede navigation and recreational use of waterways.

It already clogs large numbers of waterways in California, Florida and the Gulf Coast and is found in Europe and Iceland, as well as its native Asia.

The hydrilla strain found on the Potomac, unlike the Asian and European varieties, can propogate sexually, as well as by roots, buds, runners and broken fragments.

The corps is expected to propose several experiments to control hydrilla on the Potomac, but Anderson said that, "like gypsy moths a forest pest , there is no known way to eradicate" it.

And there is no approved herbicide that can kill hydrilla in the moving waters of a large river, said Anderson.

Hydrilla is not the first aquatic plant explosion on the Potomac to alarm area officials. Milfoil, which spread dramatically in the late 1960s, is no longer considered a threat, Anderson said. And water chestnuts also had a population explosion, but for unknown reasons have disappeared, he said.