Trial balloons and reports of discontent are clouding the skies of Alexandria as the city prepares for next year's crucial mayoral race. Mayor Frank E. Mann, the sharp-tongued incumbent, has announced his intention to seek a fourth three-year term, churning up in his wake two potentially strong challengers.

Charles E. Beatley, a former two-term mayor and City Council member, is doing what he calls "a little research to see if there is a need for competition." Beatley said Tuesday his research will be finished in about two weeks, and city hall insiders think he's going to formally enter the race for mayor.

The other serious children floating trial balloons is Margaret (Marlee) Inman, a civic activist and member of the Virginia state Health Services Coordinating Committee. Inman, a former administrative assistant to Beatley when he was mayor, said she would not run if Beatley announced that he will do so. In the meantime, hers is a "possible candidacy," she said.

Both would-be candidates cite as their prime motivation for running what they claim is Mann's abrasive manner in dealing with the council, City Manager Douglas Harman and citizens.

"I'm concerned about the environment of the council itself and its productivity," Beatley said. "The key to productivity is a good interpersonal relationship between the mayor and the council, and the mayor and the city staff, headed by the city manager. The mayor is a member of the council, he's a legislator, not an administrator." Beatley claims Mann has tried to throw this relationship out of balance.

Inman, who currently is the administrative assistant to state Sen. Wiley F. Mitchell Jr. (R-Alexandria), said that Mann had caused "a lack of harmony" on the council. "There's tension between the city manager and the mayor. Just from a good management point of view, it's easier to get things done when there's harmony. After all this time there is no consensus on the council," and there should be, she said.

"What do they want, eight yes men?" Mann said, referring to the members of the council, which includes three women. "These stores of discontent and friction are being spread by my political enemies. They can't hurt me by this, but they can hurt" others, he said. Off the record, Mann named the people he regards as his political enemies. Off the record,those individuals agreed they don't like him, either.

Some of the background to this donnybrook is this: Alexandria is one of the most swiftly changing communities in the Washington metropolitan area, a city that is increasingly being seen as a pleasant place to live and a terrific place to make money in real estate.

A community of 119,000 people, its courthouse and legal circles have been ruled for years by an "old boy" network of folks who once had a strong hand in the politics of the city.

The recent indictment of Commonwealth's Attorney William L. Cowhig on charges of bribery and illegal gambling, however, have seemed to some to serve notice that the old days are gone, regardless of the outcome of Cowhig's trial.

Another indication of the changing scene in the town are the long-delayed plans for the remodeling or upgrading of the various Torpedo Factory buildings, which currently sit astride the waterfront like green eyesores.

Nine developers will shortly present their redevelopment plans to the City Council, whose members will then decide to which firm they will sell all or some of the buildings for development.

The city's homeowners comprise 25 percent of the population, but contribute more than 60 percent of its $80 million budget. The city has a sizeable low-and moderate-income population. Through changes in housing patterns, these people are increasingly being squeezed out of town to make way for higher income families.

Against this background, Mann's conduct of the council is being raised by Beatley and Inman as an issue.

Mann, 58, who likes to wear country club colored clothes to council meetings, can often be abrasive with council members or citizens whose arguments he deems too lengthy. He is as constant as the morning in asking City Manager Douglas Harman for a line-by-line breakdown of every single dollar being spent for social services.

He does keep the council train running on time, a mixed blessing to his criticx, who ruefully remember that when the more relaxed Beatley was mayor, council sessions sometimes lasted until 1 a.m.

Mann's business life has been the subject of criticism. The owner of a company in which Mann says he is a full partner owes about $24,000 in delinquent real estate taxes and penalties on valuable riverfront property, a state of affairs that, whatever its legal outcome, casts a strange image on the increasingly civic minded council.

Last week, Beatley met with Mann to talk about the mayor's race, a unique meeting which Beatley said is "just politics." Whatever was said at the meeting, and both men resort to their mutual support of good government in describing it. Mann has emphatically let it be known that he is in the race to stay.

A second remarkable meeting was set up which was supposed to include Harman, but Harman backed out, saying it would be "inappropriate" for him to attend. Apparently, the meeting had to do with the allegations of poor rapport between Harman and Mann, which Mann said were nothing more than rumors, and untrue at that.

"I have never asked the city manager to resign. . . but I wouldn't be surprised if he was ambitious enough to think about going elsewhere at some point," Mann said.

The mayor's job pays $8,200 annually. The last filing day for both Republicans and Democrats is Jan. 2, with the primary held on March 6 and the general election on May 1. Independent candidates can file until March 6.

Mann, a former Democrat, is currently an Independent. Beatley, a Democrat, says he might consider running as an Independent. Inman has been privately encouraged by some Republicans, and both parties are expected to field candidates.