Bulletin of the American Physical Society
2006 59th Annual Meeting of the APS Division of Fluid Dynamics
Sunday–Tuesday, November 19–21, 2006; Tampa Bay, Florida
Session KP: Turbulence Theory II |
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Chair: Gregory Eying, Johns Hopkins University Room: Tampa Marriott Waterside Hotel and Marina Meeting Room 12 |
Monday, November 20, 2006 5:15PM - 5:28PM |
KP.00001: Heliccity in isotropic turbulence Yeontaek Choi, Changhoon Lee We are interested in helicity in isotropic turbulence in this study. Especially, intermittency and helicity are interesting objectives. We investigated helicity in isotropic turbulence with DNS, which the way to show is slightly different from the previous studies interested in joint spectrum of helicity with energy. First, we check the angles between velocity and vorticity of fluid particles, since the angles give contribution to alignment of velocity and vorticity. But we did not find evidences that the angles are related to intermittency of helicity by now. Second, we looked for coherent structures in isotropic turbulence, and compared to helicity. In this investigation, we verified through DNS that soliton-like structures are present in strong region of coherent structures and helicity. Third, we continued to observe relation between acceleration and helicity. Their similarities in statistics are easily deduced through analytic formula. But in this research, additionally, we employed multi-fractality and saddle point method to identify the relation. [Preview Abstract] |
Monday, November 20, 2006 5:28PM - 5:41PM |
KP.00002: Helicity creation and annihilation Robert M. Kerr, Darryl D. Holm Helicity in vortex structures and spectra is studied in the developmental stages of a numerical simulation of the Navier-Stokes equations using 3D visualisations and spectra. This presentation focuses upon two phases just before vortex tubes and a true cascade form. First, during nearly inviscid Euler dynamics strong helicity fluctuations appear on transverse vortex sheets as helicity of opposite sign is expelled for the region of strongest interactions. Simultaneously, opposite signs also develop in neighboring bands of the helicity co-spectrum. Then, after the first sign of viscous reconnection, the spectral fluctuations appear to move to higher wavenumbers and dissipate. As reconnection progresses, the flow of helicity along the vortices reverses, and the sheets roll-up into new transverse vortex tubes with oppositely signed helicity. [Preview Abstract] |
Monday, November 20, 2006 5:41PM - 5:54PM |
KP.00003: Intermittent dissipation field in multi-mode stretched-spiral vortex Kiyosi Horiuti, Takeharu Fujisawa The property of the stretched spiral vortex (SSV) (Lundgren 1982) is studied using DNS data of homogeneous isotropic and shear turbulence and the entire process of its creation, growth and annihilation is revealed. SSV is composed of three modes of configurations regarding the alignment of the vorticity vectors on the tube in the core region of SSV and the spiral sheets which emanate from the core, and all three modes are indeed identified. It is shown that the differential rotation induced by the tube and that self-induced by the sheets causes the vortex sheets in the spiral to continually tighten. With the tightening of the spiral turns of the spiral sheets, the sheets are stretched to extreme length ($\le 2 \overline{\eta}$, where $\overline{\eta}$ is the averaged Kolmogorov length). Intense turbulent energy cascade and dissipation are caused associated with this stretching of the sheets in accordance with Lundgren (1982), while no appreciable dissipation is generated in the core region. As a result, the local dissipation rate $\varepsilon$ and Kolmogorov length $\eta$ exhibit strong intermittency. Therefore, the eduction of the dissipation field is critically dependent on the grid resolution (Schumacher, Sreenivasan \& Yeung 2005), and the grids with at least $1024^3 $ or $k_{\mathrm{max}} \overline{\eta} \approx 4.0$ ($k_\mathrm {max}$ is the largest wavenumber) is indispensable for a precise capture of the spiral turns and dissipation field at $R_\lambda \approx 78.0$. [Preview Abstract] |
Monday, November 20, 2006 5:54PM - 6:07PM |
KP.00004: Spontaneous generation of vortex crystals from forced 2-D homogeneous turbulence Javier Jim\'enez, Alan Guegan The long-term limit of statistically stationary two-dimensional turbulence is known to depend on the form of the large-scale forcing. That effect is studied systematically by continuously varying the forcing from deterministic to Brownian in direct numerical simulations in doubly-periodic boxes. As expected this switches on or off the enstrophy cascade and the presence of strong coherent structures, but the transition is not monotonic. Under intermediate forcing conditions, the flow evolves to a stationary vortex crystal with triangular lattice, which appears to be stable and to last indefinitely. Deterministic forcings frustrate crystallization through the formation of fast-moving dipoles, and very random ones melt the crystal. The relation with previous experimental observations in other 2D systems, such as highly magnetized plasmas and Bose-Einstein condensates, will be discussed. [Preview Abstract] |
Monday, November 20, 2006 6:07PM - 6:20PM |
KP.00005: The Cascade of Circulations in Fluid Turbulence G. Eyink, H. Aluie Kelvin's Theorem (1869) on conservation of circulations is an essential ingredient of G. I. Taylor's theory of turbulent energy dissipation by vortex-line stretching. We have proposed [1] a novel physical effect---a ``cascade of circulations''---that leads to breakdown of circulation conservation in high Reynolds-number turbulence. Our theory is based upon an effective equation for large-scale ``coarse-grained'' velocity, which contains a turbulence-induced ``vortex-force'' that can violate Kelvin's Theorem. We show that singularities of sufficient strength, which exist in turbulent flow, can lead to non-vanishing dissipation of circulation for an arbitrarily small filtering length. This result is an analogue for circulation of Onsager's theorem on energy dissipation for singular Euler solutions. The physical mechanism of the breakdown of Kelvin's Theorem is diffusion of lines of large-scale vorticity out of the advected loop. This phenomenon is a classical analogue of Josephson-Anderson phase-slip in superfluids due to quantized vortex lines. We use locality of the circulation cascade to develop concrete expressions for the turbulent vortex-force by a multi-scale gradient-expansion. We point out a related cascade of magnetic-flux in magnetohydrodynamic (MHD) turbulence and its possible role for fast magnetic reconnection in astrophysics [2]. Supported by NSF grant \# ASE-0428325 at Johns Hopkins University. [1] G. L. Eyink, Comptes Rendus Physique, 7: 449-455 (2006). physics/0605014; Phys. Rev. E, submitted (2006). physics/0606159 [2] G. L. Eyink \& H. Aluie, Physica D, submitted (2006). physics/0607073 [Preview Abstract] |
Monday, November 20, 2006 6:20PM - 6:33PM |
KP.00006: Remarks on the Frisch framework of hydrodynamic turbulence and the quasi-Lagrangian formulation Eleftherios Gkioulekas In this talk, we revisit the claim that the Eulerian and quasi- Lagrangian same time correlation tensors are equal. This statement allows us to transform the results of an MSR quasi- Lagrangian statistical theory of hydrodynamic turbulence back to the Eulerian representation. We define a hierarchy of homogeneity symmetries between the local homogeneity of Frisch and global homogeneity. It is shown that both the elimination of the sweeping interactions and the derivation of the 4/5-law require a homogeneity assumption stronger than local homogeneity but weaker than global homogeneity. The quasi- Lagrangian transformation, on the other hand, requires an even stronger homogeneity assumption which is many-time rather than one-time but still weaker than many-time global homogeneity. We argue that it is possible to relax this stronger assumption and still preserve the conclusions derived from theoretical work based on the quasi-Lagrangian transformation. [Preview Abstract] |
Monday, November 20, 2006 6:33PM - 6:46PM |
KP.00007: Navier-Stokes dynamics on a differential one-form Troy L. Story After transforming the Navier-Stokes dynamic equation into a characteristic differential one-form on an odd-dimensional differentiable manifold, exterior calculus is used to construct a pair of differential equations and tangent vector(vortex vector) characteristic of Hamiltonian geometry. A solution to the Navier-Stokes dynamic equation is then obtained by solving this pair of equations for the position $x^k $ and the conjugate to the position ${\mathbf{b}}_k $ as functions of time. The solution ${\mathbf{b}}_k $ is shown to be divergence-free by contracting the differential 3-form corresponding to the divergence of the gradient of the velocity with a triple of tangent vectors, implying constraints on two of the tangent vectors for the system. Analysis of the solution ${\mathbf{b}}_k $ shows it is bounded since it remains finite as $\left| {x^k } \right| \to \,\infty $, and is physically reasonable since the square of the gradient of the principal function is bounded. By contracting the characteristic differential one-form with the vortex vector, the Lagrangian is obtained. [Preview Abstract] |
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