H. Miura

S. Kida

National Institute for Fusion Science (NIFS-Repository)

§ 15. Identification of Low-Pressure Vortices Miura, H. and Kida, S. Developing identification and extraction schemes of fluid motions is quite significant in order to in-vestigate complex plasma behaviors by means of numerical simulation. Among various fluid mo-tions, a vortex may be one of the most impor-tant one. For example, a vortex can twist mag-netic field lines, to cause magnetic reconnections. However, in spite of great endeavor by many re-searchers for past two or three decades, we have not reached to consensus about how to define a vortex yet. Although many methods such as streamlines, Q- and ~-definitions have been de-veloped to identify vortices, they have as much insufficiency as their advantages. (Consult with Kida and Miura[2] and references therein to see an overview on this topic, including the methods referred above.) Aiming at providing an objective definition of vortices, we have developed a method named the Sectional-Pressure-Minimum and Swirl (SPMS) method.[1, 2, 3] The SPMS method identifies a)central axes of swirling motions with sec-tional minimum of pressure and b )swirling re-gions around these central axes. The outline of this method is as follows. For simplicity, we restrict ourselves to a three-dimensional, incom-pressible and neutral fluid. First, we investigate the three real eigenvalues of the pressure hes-sian 8 2p/8xi8xj on each of grid points of a nu-merical simulation where p is the pressure of a fluid. Having two positive eigenvalues of the pres-sure hessian means existence of a sectional mini-mum of the pressure on the plane normal to the eigenvector associated with the third (the small-est) eigenvalue. By choosing the sectional min-ima of the pressure which are located sufficiently close to the grid points and imposing a swirling condition[2, 3] on them, candidates of central axes of low-pressure vortices are prepared. Then, we the have central axes by connecting these candi-dates. Since the swirling condition is expressed by a negative discriminant, D < 0, of the two-dimensional velocity-gradient tensor which is ob-238 tained by projecting flow field on the planes of the sectional-pressure-minima, swirling regions of these low-pressure vortices are given by the area with negative D. The SPMS method is applied to the simula-tion of a homogeneous and isotropic turbulence with number of grid points N 3 = 1283 • In Fig. 1, swirling axes of low-pressure vortices and swirling regions are presented. Since the whole swirling re-gions occupy more than 40% of the entire volume and look space-filling, only some typical swirling regions are presented in Fig. 1. By investigating spans of each of swirling vortices, it was found that typical span of cross sections of swirling vortices is about eight times of the Kolmogorov length scale. Figure 1: Central axis and swirling regions of ho-mogeneous and isotropic turbulence References [1] H. Miura and S. Kida: J. Phys. Soc. Jpn. 66 (1997) 1331. [2] S. Kida and H. Miura, to appear in Eur. J. Fluid Mech.B. [3] S. Kida and H. Miura: to appear in J. Phys. Soc. Jpn. 

Identification of Low-Pressure Vortices

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