Combustor systems with liners having improved cooling hole patterns

A combustor liner assembly includes a liner and a first group of cooling holes formed in the liner and having an increasing density in a downstream direction. The first group of cooling holes include a generally circumferential first row of cooling holes, a generally circumferential second row of cooling holes immediately downstream from, consecutive to, and separated from the first row at a first distance, a generally circumferential third row of cooling holes immediately downstream from, consecutive to, and separated from the second row at a second distance, and a generally circumferential fourth row of cooling holes immediately downstream from, consecutive to, and separated from the third row at a third distance. The first distance is greater than the second distance and the third distance, and the second distance is greater than the third distance.