Sounds a bit like tires spinning on slick or dusty road surfaces, or worn tires. My wife's car does this at lights a lot, the paint thy use for striping the lines gets slick here or dusty, and she will spin her tires when pulling away from a light.
2013 JKU Sport, billet, auto, 3.73, LSD, 315/75/16 Duratracs on MB 72, 10A springs, Bushwacker flatties
Sold - 2005 TJ, red, auto, 3.73, 33" Duratracs, 4" lift
Ice storm casualty in 2007 - 2003 TJ, green, auto, 3.73, 33" Duratracs, 4" lift