A combustor for a detonation engine includes a radially outer wall extending along an axis; a radially inner wall extending along the axis, wherein the radially inner wall is positioned at least partially within the radially outer wall to define an annular detonation chamber having an inlet for fuel and oxidant and an outlet; a cooling flow passage defined along at least one of the radially outer wall and the radially inner wall and comprising at least two axially spaced cooling flow passage sections, whereby a different cooling rate can be implemented in the at least two axially spaced cooling flow passage sections.