A turbine engine comprising a seal formed between at least two blades in the turbine of the turbine engine, a first turbine blade and a second turbine blade, wherein one of the turbine blades comprises a turbine rotor blade and the other turbine blade comprises a turbine stator blade, and wherein a trench cavity and the seal are formed between the first turbine blade and the second turbine blade when first turbine blade is circumferentially aligned with the second turbine blade, the seal comprising: a cutter tooth and a honeycomb; wherein: the cutter tooth comprises an axially extending rigid tooth positioned on one of the first turbine blade and the second turbine blade and the honeycomb comprises an abradable material that is positioned on the other of the first turbine blade and the second turbine blade; and the cutter tooth and the honeycomb are positioned such that each opposes the other across the trench cavity when the first turbine blade is circumferentially aligned with the second turbine blade, characterized in further comprising a cooling air channel that is formed within the turbine blade on which the honeycomb is attached and configured to deliver a supply of cooling air to surface of the honeycomb that is attached to the blade; wherein: the honeycomb and the cooling air channel are configured such that, in operation, an air curtain is formed within the trench cavity that prevents at least some ingestion of working fluid into the trench cavity; the cutter tooth is formed to deflect the flow of cooling air from the honeycomb toward the opening of the trench cavity and into flow of working fluid; and the outer edge of the cutter tooth is positioned at a radial position that is inboard of the radial center of the honeycomb such that, in operation, a greater percentage of the cooling air leaving the honeycomb strikes outboard of the cutter tooth and is thereby deflected toward the opening of the trench cavity and into the flow of working fluid.. a cutter tooth and a honeycomb; wherein: the cutter tooth comprises an axially extending rigid tooth positioned on one of the first turbine blade and the second turbine blade and the honeycomb comprises an abradable material that is positioned on the other of the first turbine blade and the second turbine blade; and the cutter tooth and the honeycomb are positioned such that each opposes the other across the trench cavity when the first turbine blade is circumferentially aligned with the second turbine blade, the cutter tooth comprises an axially extending rigid tooth positioned on one of the first turbine blade and the second turbine blade and the honeycomb comprises an abradable material that is positioned on the other of the first turbine blade and the second turbine blade; and the cutter tooth and the honeycomb are positioned such that each opposes the other across the trench cavity when the first turbine blade is circumferentially aligned with the second turbine blade, characterized in further comprising a cooling air channel that is formed within the turbine blade on which the honeycomb is attached and configured to deliver a supply of cooling air to surface of the honeycomb that is attached to the blade; wherein: the honeycomb and the cooling air channel are configured such that, in operation, an air curtain is formed within the trench cavity that prevents at least some ingestion of working fluid into the trench cavity; the cutter tooth is formed to deflect the flow of cooling air from the honeycomb toward the opening of the trench cavity and into flow of working fluid; and the outer edge of the cutter tooth is positioned at a radial position that is inboard of the radial center of the honeycomb such that, in operation, a greater percentage of the cooling air leaving the honeycomb strikes outboard of the cutter tooth and is thereby deflected toward the opening of the trench cavity and into the flow of working fluid.. the honeycomb and the cooling air channel are configured such that, in operation, an air curtain is formed within the trench cavity that prevents at least some ingestion of working fluid into the trench cavity; the cutter tooth is formed to deflect the flow of cooling air from the honeycomb toward the opening of the trench cavity and into flow of working fluid; and the outer edge of the cutter tooth is positioned at a radial position that is inboard of the radial center of the honeycomb such that, in operation, a greater percentage of the cooling air leaving the honeycomb strikes outboard of the cutter tooth and is thereby deflected toward the opening of the trench cavity and into the flow of working fluid..