The growth of the lower hybrid drift instability (LHDI) in unstable current sheets induces a fluid velocity shear that drives a Kelvin-Helmholtz instability (KHI). The KHI results in kinking of the current sheet, so that any subsequent magnetic reconnection across the current sheet must occur in three dimensions. While this increases the complexity of modeling reconnection, it is of interest for its possible resolution of the stability to tearing of current sheets with a perpendicular magnetic field. Identification of the role of the LHDI in current sheet kinking required advances in simulation technique that allowed simulations at more realistic mass ratio and long time and length scales. Confidence in the results is strongly enhanced by confirmation with a standard plasma simulation using massively parallel computation. The results of this study have obvious relevance not only to magnetic reconnection and substorms in the Earth's magnetotail, where the LHDI has been observed, but also where thin current sheets occur, such as the solar corona. (C) 2003 American Institute of Physics.