Most of the seats are sold out, to passengers who will get "commemorative 'flare,'" including Southwest viewing glasses.
Also to be served on the flights will be themed cocktails: a Bloody Mary called Red Sky, a mimosa-like libation called Stargazer, and a vodka and OJ drink called Sun Flare.
"They're not special flights but they're flights we're making special," said Southwest spokesman Brad Hawkins. While the view from the ground could be obscured by clouds, a flight "gets you above all that so you'll at least see something," he said.
Looking at all airlines, NASA astronomer Sten Odenwald found 100 scheduled flights that would be over the path of totality around the time of the eclipse, then conducted a series of calculations of their flights paths and timing to find flights that would have the best viewing locations.
He found a number of flights on multiple carriers including Delta Air Lines that he estimates would come close to the path of totality "at about the right time."
Atlanta-based Delta's Flight 2466 from Portland to Atlanta follows the path of totality of the eclipse, though it breaks off after getting to Tennessee. The flight is scheduled to depart Portland at 8:45 a.m. and arrive in Atlanta at 4:29 p.m.
Odenwald wrote that "it is fun to consider that if you happened to be on just the right flight, you may be lucky enough to see at least part of the total solar eclipse."
And passengers on thousands of flights -- with a window seat, at least -- will likely have an opportunity to see at least a partial eclipse.
Alaska Airlines held a contest for people to win seats on an eclipse-chasing charter flight it will operate Monday, announcing this week that a passenger in Austin and another in Charlotte are the winners. Otherwise, the charter flight is invitation only.
Those on the Alaska Airlines charter flight "will be treated to an eclipse party like no other, all from a cruising altitude of 35,000 feet above the earth and before most anyone else," according to the airline.
"As an airline, we are in a unique position to provide a one-of-a-kind experience for astronomy enthusiasts," Alaska Airlines' vice president of marketing Sangita Woerner said in a written statement.
The airline said in 2016, at the request of eclipse viewers, it adjusted a flight path of a flight from Anchorage to Honolulu for better viewing of a total solar eclipse over the Pacific Ocean.
-- Stay up to date on the latest news on Atlanta airline travel by following
Atlanta Airport News Now
7 things to know about the rare total solar eclipse crossing the nation this August
How Georgians can watch the rare total solar eclipse this summer
Georgia events related to the Aug. 21, 2017 solar eclipse
Southwest Airlines and other carriers are touting eclipse flights that trace the path of the eclipse for a good view of totality.