Turn ash into oak
Why ash? Few woods match the dramatic grain pattern of flatsawn oak, but ash comes close. Stain containing pigment catches in the pores of both ash and oak, emphasizing their similarities further.
Making the switch: Coming close to a match was as simple as staining the ash with Minwax red oak (#215). The pores of the ash will absorb more pigment from a liquid (not gel) stain than will oak. For a darker finish, sand ash to 150-grit, leaving a slightly rougher surface where the particles of stain pigments can collect. Use a dye if you want minimal grain contrast.