This research aims to apply Beltrami compressible flows in the identification of vortices, according to different kinematic identification criteria, and to weave discussions about the regions identified in the molds found in Andrade (2007) and Andrade (2008). Beltrami flows are a class of flows that have been the subject of intense interest by many researchers. Many studies have been carried out on incompressible Beltrami flows, while similar analyzes based on the compressible case are much rarer, which motivated this work. Analytical steady state incompressible solutions of Euler's equations that satisfy the condition of a Beltrami flow have applications in the study of field line topology, in the context of dynamical systems (Arnold, 1989; Arnold and Khesin 1998), in the study of turbulence in fluids, and in the generation of magnetic fields (Arnold and Khesin, 1998; Moffatt, 1986; Constantin and Majda, 1988; Arnold, 2014; Andrade, 2008). In the case of compressible flow, Beltrami flows were applied by Govorukhin, Morgulis et al. (1999) and by Govorukhin (2003), using the fundamentals developed by Morgulis et al. (1995), to analyze the topology of orbits obtained through Poincaré maps. The velocity field described in section 2.1 (The CABC Flow) was applied to obtain the vortices identified according to the criteria established in Section 3 (Methods of identification of vortices). The vortices were extracted through the implementation of the CABC Flow, and the calculation of each of the scalar fields that define each of the criteria in a computational code using the MATLAB software, on a three-dimensional domain varying between 0 and 2π in the 3 x coordinate directions, y, z, with step 0.2. The vortex views are slices of the scalar fields identified as volumes according to the three criteria obtained through the Isocaps reference function in a common configuration PC. As a summary of this discussion, different identification methods occupy different regions, to a greater or lesser extent, with greater or lesser magnitude of scalar fields. This type of flow structure analysis is useful to extend the understanding of flow dynamics and can support, e.g., turbulence models (Fernandes et al., 2012). Finally, additional simulations of the identification criteria discussed here and other identification criteria on the CABC Flow, on a wide spectrum of functions and parameters that define the flow, as well as simulations of experimental compressible laboratory flows from data obtained by Particle Image Velocimetry (PIV) is needed to deepen the brief impressions gathered here.
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