A system, comprising: a gas turbine engine, comprising: a combustor section having one or more combustors configured to generate combustion products; a turbine section having one or more turbine stages between an upstream end and a downstream end, wherein the one or more turbine stages are driven by the combustion products; an exhaust section disposed downstream from the downstream end of the turbine section, wherein the exhaust section has an exhaust passage configured to receive the combustion products as an exhaust gas; and a mixing device disposed in the exhaust section, the mixing device being configured to divide the exhaust gas into a first exhaust gas and a second exhaust gas, and to combine the first and second exhaust gases in a mixing region to produce a mixed exhaust gas, wherein the mixing device comprises: a first section configured to convey the first exhaust gas to the mixing region, wherein the first section comprises a lobe mixer having an annular sinusoidal shape with alternating first and second open-ended passages, the first open-ended passages being configured to direct a first portion of the first exhaust gas away from a longitudinal axis of the mixing device, and the second open-ended passages being configured to direct a second portion of the first exhaust gas toward the longitudinal axis; and a second section configured to convey the second exhaust gas to the mixing region, wherein the second section circumferentially surrounds the first section. a combustor section having one or more combustors configured to generate combustion products; a turbine section having one or more turbine stages between an upstream end and a downstream end, wherein the one or more turbine stages are driven by the combustion products; an exhaust section disposed downstream from the downstream end of the turbine section, wherein the exhaust section has an exhaust passage configured to receive the combustion products as an exhaust gas; and a mixing device disposed in the exhaust section, the mixing device being configured to divide the exhaust gas into a first exhaust gas and a second exhaust gas, and to combine the first and second exhaust gases in a mixing region to produce a mixed exhaust gas, wherein the mixing device comprises: a first section configured to convey the first exhaust gas to the mixing region, wherein the first section comprises a lobe mixer having an annular sinusoidal shape with alternating first and second open-ended passages, the first open-ended passages being configured to direct a first portion of the first exhaust gas away from a longitudinal axis of the mixing device, and the second open-ended passages being configured to direct a second portion of the first exhaust gas toward the longitudinal axis; and a second section configured to convey the second exhaust gas to the mixing region, wherein the second section circumferentially surrounds the first section. a first section configured to convey the first exhaust gas to the mixing region, wherein the first section comprises a lobe mixer having an annular sinusoidal shape with alternating first and second open-ended passages, the first open-ended passages being configured to direct a first portion of the first exhaust gas away from a longitudinal axis of the mixing device, and the second open-ended passages being configured to direct a second portion of the first exhaust gas toward the longitudinal axis; and a second section configured to convey the second exhaust gas to the mixing region, wherein the second section circumferentially surrounds the first section.