An enhanced cooling system for the downstream end of a combustor liner assembly is provided. The downstream end region of the combustor liner assembly is formed by a subassembly comprising an outer tubular member, an inner tubular member and a middle band. The middle band includes a plurality of undulations having alternating peaks and valleys. The middle band is operatively positioned between the inner and outer tubular members to form a plurality of elongated cooling passages. A turbulence generator is provided along each of the cooling passages and extends radially inward from a portion of the peaks such that the turbulence generator and the valleys contact an outer peripheral surface of the inner tubular member. The surface area of the middle band that is in contact with the inner tubular member is greater than the surface area of the middle band that is in contact with the outer tubular member.