§S7. Interaction between a Columnar Vortex and External Turbulence

The interaction between a columnar vortex and exter-llal turbulence is investigated numerically. As the colum-nar vortex) the Lamb-Oseen vortex is used. The columnar vortex is immersed in an initially isotropic homogeneous turbulence field, which itself is produced by a direct nu-merical simulation of decaying turbulence. Using visu-alization techniques, we investigate the formation of in-homogeneous fine turbulent eddies around the columnar vortex, the vortex-core deformations and the dynamical evolution in the passive scalar field. We investigate the dynamical evolution of the vor-tex structure and the passive scalar structure, appeared due to the isotropic homogeneous turbulence interact-ing with the columnar vortex. The characteristics of the flow field are analyzed by using several flow-visualization techniques. The statistics of the turbulence around the columnar vortex are investigated by computing the two-point energy spectrum tensors, and they are com-pared with the results of a linear rapid distortion theory (RDT) [11. The growth of the velocity and vorticity dis-turbances are proportional to to. 9 and t 1 respectively. Al-though the results are qualitatively consistent with RDT, that do not agree quantitatively with the prediction of RDT(cx t2). We solve the Navier-Stokes equation for incompressible fluids and the transport equation for the passive scalar (such as a passive temperature field or a dye) under pe-riodic boundary conditions with period 41r. A spectral method is. used to solve the equations. The time integra-tion is performed using the fourth order Runge-Kutta-Gill method. The simulations are done with resolutions of 2563 and 5123. The columnar vortex is immersed in an initially isotropic homogeneous turbulence field. which itself is produced numerically by a direct numeric ~ sim-ulation of decaying turbulence. As the columnar vortex, we use the Lamb-Oseen vor-tex. In cylindrical coordinates, the velocity components of the Lamb-Oseen vortex are defined b