This study uses a series of numerical simulations to examine the structure of the wake of the Hawaiian island of Kauai. The primary focus is on the conditions on 26 June 2003, which was the day of the demise of the Helios aircraft within Kauai's wake. The simulations show that, in an east-northeasterly trade wind flow, Kauai produces a well-defined wake that can extend 40 km downstream of the island. The wake is bounded to the north and south by regions of strong vertical and horizontal shear - that is, shear lines. These shear lines mark the edge of the wake in the horizontal plane and are aligned approximately parallel to the upstream flow direction at each respective height. The highest-resolution simulations show that these shear lines can become unstable and break down through Kelvin - Helmholtz instability. The breakdown generates turbulent eddies that are advected both downstream and into the recirculating wake flow. Turbulence statistics are estimated from the simulation using a technique that analyzes model-derived structure functions. A number of sensitivity studies are also completed to determine the influence of the upstream conditions on the structure of the wake. These simulations show that directional shear controls the tilt of the wake in the north - south plane with height. These simulations also show that at lower incident wind speeds the wake has a qualitatively similar structure but is less turbulent. At higher wind speeds, the flow regime changes, strong gravity waves are generated, and the wake is poorly defined. These results are consistent with previous idealized studies of stratified flow over isolated obstacles.