Vortical Structure of Turbulent Shear Flows Studied by Vortex Dynamics Simulation

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1. Evolution of square vortex rings with rounded corners was simulated by a vortex blob method, in which the connectivity of vortex filaments is not explicitly maintained, to obtain patterns of deformation and the exetnt to which dynamical invariants of the three-dimensional inviscid vortex motion are really conserved. The simulation showed that the invariants were conserved until their catastrophic increase took place. The kinetic energy was found to serve as the most stringent criterion to discuss the conservation of the invariants. The time when the catastrophic bahavior appeared increased with increasing radius of core of the vortex blobs and with increasing radius of curvature of the corners. Evolution of topology of the vortex rings was obtained and discussed.2. A vortex dynamics simulation was made on the deformation of pseudoelliptical vortex rings which consists of two parallel line segments connected by two semicircles of the same radius, the major-to-minor axis ratio being b … More etween 2 and 20. The deformation had four fundamental patterns depending on the aspect ratio : the periodic axis switching ; the splitting into two vortex rings after the axix switching ; the splitting into two vortex rings without the axis switching ; the splitting into three vortex rings without the axis switching. The last two patterns are expected to lead to further axis switching and eventual splitting into two vortex rings at larer times. This was confirmed by a flow visualization experiment.3. An inviscid vortex dynamics simulation of interaction of several circular vortex rings produced the power spectrum which had a part of the Kolmogorov -5/3 power law. The enstrophy spectrum, which is equivalent to the dissipation spectrum in homogeneous turbulence, had a part of the 1/3 power law in the same wavenumber range. This study is among the first to show the -5/3 power spectrum as a result of the inviscid interaction of several, not many, vortex rings. The wavenumber range of the -5/3 power law slightly depends on the number of the vortex rings and their initial configuration, being wider for smaller radius of core of the vortex rings. A uniform distribution of high-vorticity regions appears to be essential to have the -5/3 power law. Five invariants of the inviscid vortical motion, i. e. The total energy, total momentum, total angular momentum, total helicity and total vorticity were maintained constant within tolerable deviations from the corresponding initial valves until vorticity tends to diverge.4. The unsteady separated flow around an inclined circular disk was simulated by the vortex blob method to obtain the evolution of three-dimensional vortical structures from circular vortex rings formed by the separation from the edge of the disk. A spiral structure of the vortical wake was confirmed by the simulation in terms of the vorticity contour in planes normal to the direction of the approaching flow. Less