As a sample problem, the onset and growth of the Kelvin-Helmholtz instability was studied. This instability arises when the interface between two fluids in shear motion is perturbed, and for this problem the body forces, and , are zero. In Figure 6.2 (Color Plate), we show the development of the Kelvin-Helmholtz instability at the interface of two fluids in shear motion. In these figures, the density of the massless marker particles normalized by the fluid density is plotted on a color map, with red corresponding to a density of one through green, blue, and white to a density of zero. Initially, all the marker particles are in the upper half of the domain, and the fluids in the lower- and upper-half domains have a relative shear velocity in the horizontal direction. An finite difference grid was used. Vortices form along the interface and interact before being lost to numerical diffusion. By processing the output from the nCUBE-1, a videotape of the evolution of the instability was produced. This sample problem demonstrates that the FCT technique is able to track the physical instability without introducing numerical instability.
Figure 6.2: Development of the Kelvin-Helmholtz instability at the interface of two fluids in shear motion.