Liu et al. 2008 discuss an important consideration for models of zonal winds deep within giant planets. However, the constraints they propose for the depth of the winds are based on their prescriptions for the internal structures of the magnetic field and zonal winds. The same kinematic analysis applied to other plausible configurations would produce no constraint on the depth to which the winds extend.
Cite
@article{arxiv.0803.4298,
title = {A note on "Constraints on deep-seated zonal winds inside Jupiter and Saturn"},
author = {Gary A. Glatzmaier},
journal= {arXiv preprint arXiv:0803.4298},
year = {2009}
}