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Kelvin-Helmholtz instabilities are common in astrophysical systems, rangingfrom jet black holes up to protoplanetary accretion disk. An astrophysicalobject with strong characteristics of the Kelvin-Helmholtz instability isCaraguejo Nebula, in which the material expansion was caused by the explosionof a supernova about 1000 years ago. This instability occurs at the boundarybetween two fluids of different densities when one of the fluids acceleratedwith respect to the other. In order to study this instability, we performed asimulation with the code ATHENA Eulerian mesh. For this simulation, we considera square domain with periodic boundaries on the sides, and reflecting on theboundary of the top and bottom. The upper box is filled with a gas density{\rho}=1.0, pressure P1 = 1.0, adiabatic index {\gamma}=5/3, and velocityu1=0.03 in the x direction (to the right). The lower portion has a density{\rho}=2.0, the same pressure, velocity, and adiabatic index, only in theopposite direction to the left. Speed is defined as a sinusoidal function,which creates the initial disturbance. As a result, we observe the principle ofinstability and the formation of vortices, with well-defined ridges. Thedistinctness of the boundary between the material of high and low density iswell preserved due to the relatively low diffusion algorithm. We also note thatthe simulation evolving vortices formed from the turmoil merge.

Study of the Kelvin-Helmholtz instability through simulation with the code Athena