4 results in Papers related to Dubrulle's webinar
A physical model of turbulence cascade via vortex reconnection sequence and avalanche
- Jie Yao, Fazle Hussain
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- Published online by Cambridge University Press:
- 28 November 2019, A51
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Viscous anti-parallel vortex reconnection is studied by means of direct numerical simulation for vortex Reynolds numbers $Re$ ($\equiv \unicode[STIX]{x1D6E4}/\unicode[STIX]{x1D708}$, circulation/viscosity) up to 40 000. To suppress the inherent symmetry breaking due to the Kelvin–Helmholtz (planar jet) instability, as prevalent in prior studies, and to better explore the progression of the mechanism details, the simulation is performed by imposing symmetry and using double-precision arithmetic. We show, for the first time, the evidence of vortex reconnection cascade scenario initially proposed by Melander and Hussain (CTR Report, 1988), who suggested that the remnant threads, following the first reconnection, undergo successive reconnections in a cascade. Secondary reconnection (the details distinctly captured and visualized at a lower $Re=9000$) leads to the successive generation of numerous small-scale structures, including vortex rings, hairpin-like vortex packets and vortex tangles. As $Re$ increases, the third and higher generations of reconnection form a turbulent cloud avalanche consisting of a tangle of fine vortices. The energy is rapidly transferred to finer scales during reconnection, and a distinct - 5/3 inertial range is observed for the kinetic energy spectrum, associated with numerous resulting fine-scale bridgelets and thread filaments. In addition, we also discover an inverse cascade at large scales through the accumulation of bridgelets. The separation distance $\unicode[STIX]{x1D6FF}(t)$ before the first reconnection is found to scale as $t^{3/4}$, which is different from the typical 1/2 scaling for classical and quantum vortex filament reconnections. Both peak enstrophy and its production rate grow with $Re$ faster than the power law suggested by Hussain and Duraisamy (Phys. Fluids, vol. 23, 2011, 021701). Our simulations not only reveal the detailed mechanisms of high-$Re$ reconnection, but also shed light on the physics of turbulence cascade and present the reconnection avalanche as a realistic physical model for turbulence cascade.
Beyond Kolmogorov cascades
- Bérengère Dubrulle
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- 22 March 2019, P1
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The large-scale structure of many turbulent flows encountered in practical situations such as aeronautics, industry, meteorology is nowadays successfully computed using the Kolmogorov–Kármán–Howarth energy cascade picture. This theory appears increasingly inaccurate when going down the energy cascade that terminates through intermittent spots of energy dissipation, at variance with the assumed homogeneity. This is problematic for the modelling of all processes that depend on small scales of turbulence, such as combustion instabilities or droplet atomization in industrial burners or cloud formation. This paper explores a paradigm shift where the homogeneity hypothesis is replaced by the assumption that turbulence contains singularities, as suggested by Onsager. This paradigm leads to a weak formulation of the Kolmogorov–Kármán–Howarth–Monin equation (WKHE) that allows taking into account explicitly the presence of singularities and their impact on the energy transfer and dissipation. It provides a local in scale, space and time description of energy transfers and dissipation, valid for any inhomogeneous, anisotropic flow, under any type of boundary conditions. The goal of this article is to discuss WKHE as a tool to get a new description of energy cascades and dissipation that goes beyond Kolmogorov and allows the description of small-scale intermittency. It puts the problem of intermittency and dissipation in turbulence into a modern framework, compatible with recent mathematical advances on the proof of Onsager’s conjecture.
A tent model of vortex reconnection under Biot–Savart evolution
- Yoshifumi Kimura, H. K. Moffatt
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- 17 November 2017, R1
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Vortex reconnection under Biot–Savart evolution is investigated geometrically and numerically using a tent model consisting of vortex filaments initially in the form of two tilted hyperbolic branches; the vortices are antiparallel at their points of nearest approach. It is shown that the tips of these vortices approach each other, accelerating as they do so to form a finite-time singularity at the apex of the tent. The minimum separation of the vortices and the maximum velocity and axial strain rate exhibit nearly self-similar Leray scaling, but the exponents of the velocity and strain rate deviate slightly from their respective self-similar values of $-1/2$ and $-1$; this deviation is associated with the appearance of distinct minima of curvature leading to cusp structures at the tips. The writhe and twist of each vortex are both zero at all times up to the instant of reconnection. By way of validation of the model, the structure of the eigenvalues and eigenvectors of the rate-of-strain tensor is investigated: it is shown that the second eigenvalue $\unicode[STIX]{x1D706}_{2}$ has dipole structure around the vortex filaments. At the tips, it is observed that $\unicode[STIX]{x1D706}_{2}$ is positive and the corresponding eigenvector is tangent to the filament, implying persistent stretching of the vortex.
The dynamics of vorticity tubes in homogeneous turbulence
- A. Vincent, M. Meneguzzi
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- 26 April 2006, pp. 245-254
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Analysis of data from a direct simulation of statistically steady homogeneous turbulence suggests that the vorticity tubes, which constitute the main structure of the vorticity field, are produced by shear instabilities. This is confirmed by a decay calculation, in which vorticity sheets appear at first, and then roll up to form the first tubes. These instabilities seem to be at least as important as vortex stretching in transferring energy from large to small scales.