If everything goes as expected, by mid-decade it should be hard to walk around in Southern Virginia without bumping into a convention center.

Norfolk has one. Virginia Beach is building one. And Richmond has just triumphed in a long and difficult legal battle that delayed construction of a convention center here for many years.

What is happening in Southern Virginia is happening in cities around the nation. Perhaps no other single gimmick has been sold as an economic tonic so often to so many places as has been convention centers.

What the cities in Southern Virginia have to offer is slightly different from cities such as Washington and Atlanta, which have also succumbed to visions of convention-generated dollars.

While Washington's convention center is expected to snag massive national convention too large to house in the city's convention hotels, Norfolk, Virginia Beach and Richmond appeal more to regional, state and small national conventions.

James Lowe, president of the American Society of Association Executives said, "norfolk doesn't have enough rooms" for major national conventions. "I'll have 5,000 delegates in the Sheraton Park (in Washington) in august." A brochure for Scope, the Norfolk center, adverties 1,000 hotel rooms with a mile of the center.

"I can't go to Norfolk," Lowe said. "I can't go south until I get to Atlanta."

Thirteen conventions did go to Norfolk last year, however, including the Virginia Restaurant Association, the Virginia Education Association, the Eastern Regional Machine Dealers Association, the Worldwide Church of God, the International Association of Flying Farmers (who parked 500 private planes at the Norfolk airport), the Doberman Pinscher Clubs of America, the International Arabian Horse Fair, the Central Intercollegiate Athletic Association and the American Contract Bridge League.

"Last year we estimate that convention attendees spent about $18 million in Norfolk," said Jeter Walker, director of the Norfolk Convention and Visitors Bureau. That included 162 groups.

"If Scope weren't here, it would be that much less, and city tax revenues would be down by about $1 million," he said.

The building operates at a deficit as do virtually all convention centers, but Walker and C. Edwin Bell, who directs the center, maintain that the "building almost pays for itself more than four times over because of the business brought in."

The building, a handsome concrete dome that includes a 25,000-square-foot convention hall, a 60,000-square-foot exhibition hall, a 2,355-seat theater and more than 20 meeting rooms, was dedicated in 1972. It was built on 17-acre site in the middle of slums as part of an urban renewal project, with the federal government putting up $2 for each dollar the city raised through a bond issue.

The next center to open will be in Virginia Beach. A long building that looks, in its incomplete state, like a series of quonset huts, the center is actually a 75,000-square-foot exhibition hall with meeting rooms connected to a 1,000-seat auditorium by a garden court.

The center will host its first convention in September when 18,000 delegates from, the Mid-Atlantic Shriner Association descend on the resort, which is also the second largest city in the state. The last time the Shriners were in the city was in 1976, before the meeting became too large for the facilities on hand then.

Virginia Beach's convention center is different from others in that it is designed to accommodate conventions during the off-season, to provide profits for the tourist-serving industry from September to May. Richmond is not yet to the point of selling conventions. Last week it began to sell bonds to finance construction of its proposed convention center. The center, which will be built in a slightly shabby area of downtown Richmond, has not yet been designed.

The Richmond center originally was conceived in 1977 as part of a downtown redevlopment proposal called Project One, which also included a hotel, offices and shops. The site is almost adjacent to the Richmond Coliseum, built in 1968.

The city prevailed over opposition to the center, which came mainly from the Richmond Independent Taxpayers Association in a series of court tests, finally getting a green light from the state Supreme Court in January 1980.

Now the city is moving rapidly on the project, building a center that will cost more because construction costs have inflated while the city fought off challengers. "The total project under the old figures was expected to cost about $80 million," city manager Manuel Deese said. "With inflation that figure is about $95 million."