Turbomachine assembly with combustors having different flow directions and corresponding operating method

A turbomachine assembly includes a first combustor (30) configured to combust fuel and compressed air and a second combustor (32) configured to combust fuel and compressed air. Flow moves through the first combustor (30) in a first direction and flow moves though the second combustor (32) in a second direction different than the first direction. The first combustor (30) is axially spaced from the second combustor (32). A corresponding operating method is also provided.