By Frédéric Moisy, Javier Jiménez (auth.), SHIGEO KIDA (eds.)

Elementary vortices – these tubular swirling vortical buildings with targeted vorticity as a rule saw in different types of turbulent flows – play key roles in turbulence dynamics (e.g. enhancement of combining, diffusion and resistance) and signify turbulence records (e.g. intermittency). due to their dynamical value, manipulation of hassle-free vortices is anticipated to be potent and valuable in turbulence keep an eye on in addition to in development of turbulence modeling. the main complicated examine works on uncomplicated vortices and similar difficulties have been provided and mentioned on the IUTAM Symposium in Kyoto, Japan, 26-28 October 2004. This booklet comprises forty contributions offered there, the topics of which hide vortex dynamics, coherent constructions, chaotic advection and combining, statistical homes of turbulence, rotating and stratified turbulence, instability and transition, dynamics of skinny vortices, finite-time singularity, and superfluid turbulence. The publication may be important for readers of graduate and complicated degrees within the box of fluid turbulence.

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**Extra resources for IUTAM Symposium on Elementary Vortices and Coherent Structures: Significance in Turbulence Dynamics: Proceedings of the IUTAM Symposium held at Kyoto International Community House, Kyoto, Japan, 26-28 October 2004**

**Sample text**

1 Lamb-oseen vortex (q = −∞) Flow ﬁeld In the case of the Lamb-Oseen vortex (Takahashi et al. 2005), the columnar vortex undergoes a deformation due to the interaction, and the vortex wraps worms around its surface in a spiral structure (Fig. 2). In larger scales, we can see that a vortex has a columnar structure at the center of the region, and that it is curved. In ﬁner scales, we observe the characteristic structure of thin, tube- and ring-like shapes, which implies that the vortex rings have developed from the ﬁne-scale structure, which was input as worms in the initial turbulence.

Arrangement of the columnar vortices in the cubic box with periodic boundary conditions. 2. Numerical method We solve the Navier-Stokes equation for incompressible ﬂuids 1 ∂u + u · ∇u = − ∇p + ν∇2 u, ∂t ρ ∇·u = 0 (1) (2) and the transport equation for the passive scalar (such as a passive temperature ﬁeld or a dye) ∂s + u · ∇s = κ∇2 s ∂t (3) under periodic boundary conditions with period 4π. A spectral method is used to solve the equations. The time integration is performed using the Runge-KuttaGill method with spatial resolutions of 2563 and 5123 .

Figs. 7, respectively. 47), Fig. 6a shows that max |Φzz (r, r, t; kz , m)| at low wavenumbers is larger than at high wavenumbers. e. the normal energy cascade. 7) when the characteristic deformation of the columnar vortex is observed. Fig. 7 40 40 30 m 25 20 15 30 25 20 15 10 10 5 5 0 |Φzz|= 1e02 1e01 1e00 1e-1 1e-2 1e-3 1e-4 1e-5 1e-6 1e-7 35 m |Φzz|= 1e02 1e01 1e00 1e-1 1e-2 1e-3 1e-4 1e-5 1e-6 1e-7 35 0 0 5 10 15 20 k zr 0 0 5 10 15 20 k zr 0 Figure 6. 7. The contour lines are plotted in logarithmic scale.