A polishing pad (104, 300, 400, 500) for polishing a wafer (112, 516), or other article. The polishing pad includes a polishing layer (108) containing a plurality of grooves ((148, 152, 156)(304, 308, 324)(404, 408, 424)(520, 524, 528)) having orientations largely parallel to one or more corresponding respective velocity vectors (V1–V4)(V1′–V4′)(V1″–V4″)(V1′″–V4′″) of the wafer. These parallel orientations promote the formation of mixing wakes in a polishing medium (120) within these grooves during polishing.