Bulletin of the American Physical Society
70th Annual Meeting of the APS Division of Fluid Dynamics
Volume 62, Number 14
Sunday–Tuesday, November 19–21, 2017; Denver, Colorado
Session A9: Vortex Dynamics and Vortex Flows IVortexes
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Chair: Rodolfo Ostilla Monico, Harvard University Room: 502 |
Sunday, November 19, 2017 8:00AM - 8:13AM |
A9.00001: From vortex tubes to vortex rings: reconnections and the turbulent cascade Rodolfo Ostilla Monico, Ryan McKeown, Shmuel Rubenstein, Alain Pumir, Michael P. Brenner We numerically simulate the head-on vortex ring collision experiment of Lim and Nickels (Nature, 357:225-227), and of McKeown et al. (APS-DFD talk) in an attempt to understand the rapid formation of very fine scale turbulent fluctuations (or 'smoke') from relatively smooth initial conditions. Reynolds numbers of up to $Re = \Gamma/\nu = 7500$ are reached, where $\Gamma$ is the vortex ring circulation, and $\nu$ the kinematic viscosity of the fluid. Different perturbations to the ring vortex are added, and their effect on the generation and amplification of turbulence is quantified. The underlying dynamics of the vortex core is isolated, and compared to that arising from a simple Biot-Savart filament model. The presence of Crow and elliptic instabilities is used to explain the different dynamics: either vortex reconnection or “cloud" formation. Finally, the links between head-on vortex ring collision to finite-time singularities in the Biot-Savart equations, and to their possible relationship to finite-time singularities in the Euler equations and the turbulent cascade is analyzed. [Preview Abstract] |
Sunday, November 19, 2017 8:13AM - 8:26AM |
A9.00002: The Emergence of Small Scales in Vortex Ring Collisions Ryan McKeown, Rodolfo Ostilla Monico, Alain Pumir, Michael P. Brenner, Shmuel Rubinstein When two vortex rings collide head-on, the initially smooth flow structures rapidly become unstable as they develop complex three-dimensional dynamics that result in the vortex cores either reconnecting or breaking down into a fine-scale “turbulent cloud.” As the vortex rings first approach one another, they are stretched radially along the collision plane. The close-range interactions of the counter-rotating vortices lead to the development of perturbations in the vortex cores. Long-wavelength perturbations develop into “tents” that bridge the cores and reconnect or break down. Short-wavelength perturbations cause the cores to become locally “kinked” and break down before contacting. We use high-speed flow visualization techniques with a scanning laser sheet to reconstruct the intricate, three-dimensional dynamics of the interacting vortex cores. For both perturbation modes, we observe that the breakdown of the vortex cores is caused by the local flattening of the cores into vortex sheets, which break down into smaller vortex filaments. These secondary filaments break down again in an iterative manner to produce fine-scale turbulent “smoke.” This iterative cascade could be indicative of a possible mechanism by which kinetic energy is conveyed to small scales in turbulent flows. [Preview Abstract] |
Sunday, November 19, 2017 8:26AM - 8:39AM |
A9.00003: Interaction of shocklets and vortex surfaces in high-Mach-number Taylor-Green flows Naifu Peng, Yue Yang We simulate the evolution of vortex-surface fields (VSFs) in viscous compressible Taylor-Green flows with a range of Mach numbers ($Ma$), and quantitatively investigate the interaction of shocklets and vortex surfaces in the temporal evolution. Here the isosurface of the VSF is defined as a vortex surface consisting of vortex lines. In high-$Ma$ flows, shocklets are generated and they have strong interaction with vortex surfaces. Before vortex reconnection, the shocklets with strong contracting velocity significantly shrink the surrounding vortex surfaces, and on the other hand they are slightly curved by the vortex-induced velocity. Subsequently the shocklets cause the earlier occurrence and larger degree of vortex reconnection with increasing $Ma$. [Preview Abstract] |
Sunday, November 19, 2017 8:39AM - 8:52AM |
A9.00004: Scaling properties towards vortex reconnection under Biot-Savart evolution Yoshifumi Kimura, Keith Moffatt Reconnection of two vortex filaments under the Biot-Savart law is investigated numerically using vortex filaments in the configuration of tilted hyperbolae initially. For the numerical method, the vortices are divided into piecewise linear segments with an initial coordinate stretching by the double exponential formula, and the Biot-Savart integral is approximated by a summation over the segments with a cut-off method to deal with the singular terms. It is demonstrated that the centre parts of the hyperbolae tend to approach and accelerate to form a singularity. Even though the minimum separation of the hyperbolae, the maximum velocity and the maximum axial strain rate show clear scaling exponents close to the singularity of Leray type, the latter two exponents are slightly more singular to cause a production of inflection points and eventually cusp structures at the tips $^{[1]}$. As a validation of the model, $\lambda_2$, the second eigenvalue of the rate of strain tensor, is investigated around the vortices. It is shown that $\lambda_2$ takes negative values near the tip of the vortices for almost all the time. [1] Y. Kimura \& K. Moffatt, Scaling properties towards vortex reconnection under Biot-Savart evolution. (2017), {\it Fluid Dyn. Res.} in press. [Preview Abstract] |
Sunday, November 19, 2017 8:52AM - 9:05AM |
A9.00005: Untangling Superfluid Vortices Dustin Kleckner Previous work has shown that simple knotted vortices will untie in both viscous fluids and superfluids. Does the same behavior hold for complexly tangled vortices, irrespective or shape and topology? By simulating large numbers of vortex configurations in the Gross-Pitaevskii equation, I will show that the spontaneous unknotting of vortices is a universal feature of undriven fluids. I will also discuss the connection to conservation of helicity and topological features of the unknotting process. [Preview Abstract] |
Sunday, November 19, 2017 9:05AM - 9:18AM |
A9.00006: The influence of background shear on asymmetric vortex interactions Patrick Folz, Keiko Nomura The influence of uniform background shear, $\alpha = dU/dy$, on a pair of like-signed viscous vortices with strength ratio, $\Lambda = \Gamma_1/\Gamma_2 \leq 1$, is investigated using two-dimensional numerical simulations. A shear strength parameter is defined, $\zeta = -\alpha/\omega_{2}$, where $\omega_{2}$ is the peak vorticity of the stronger vortex. In shear-dominated flows, for sufficiently strong adverse shear ($\zeta < \zeta_{sep} < 0$), the vortices separate, and for strong magnitude shear ($|\zeta| > \zeta_{cr}$), both vortices are detrained and destroyed. The value of $\zeta_{sep}$ is found to vary with $\Lambda$ in close agreement with a point-vortex model, while $\zeta_{cr} \approx 0.20$ is approximately constant in the parameter ranges considered. In vortex-dominated flows ($\zeta_{sep} < \zeta < \zeta_{cr}$), the vortices always interact to produce a single quasi-stable vortex. The post-interaction vortex is evaluated by an enhancement factor, $\varepsilon = \Gamma_{end}/\Gamma_{2,start}$. The interaction is considered a merger if $\varepsilon > 1$ and a straining out if $\varepsilon \approx 1$. The behavior of $\varepsilon$ is effectively characterized by the ratio of starting vortex enstrophies, $Z_2/Z_1$, with key values comparable to the no-shear case. [Preview Abstract] |
Sunday, November 19, 2017 9:18AM - 9:31AM |
A9.00007: A new vortex definition for compressible and stratified flows Jie Yao, Fazle Hussain We propose an objective vortex identification method (call it `$\lambda _{\rho } $ criterion') for flows dominated by compressibility or density variation effects, where the standard $\lambda_{2} $ method is not expected to be valid. The new $\lambda_{\rho } $ criterion - which is a direct extension of $\lambda_{2} $ criterion for incompressible flow - defines a vortex to be the region where the second eigenvalue of the tensor $\mathbf{S}^{m}\mathbf{+S}^{\vartheta }$ is negative. Here, $\mathbf{S}^{m}$ is the symmetric part of the tensor product of the momentum gradient tensor $\nabla (\rho \mathbf{u})$ and the velocity gradient tensor $\nabla (\mathbf{u})$ ; $\mathbf{S}^{\vartheta }$ is the symmetric part of dilatation-momentum gradient tensor $\nabla (\vartheta \rho \mathbf{u})$; and $\vartheta \equiv \nabla \bullet \mathbf{u}$ is the dilatation rate. We demonstrate the difference between $\lambda_{\rho } $ and $\lambda_{2} $ boundaries for the compressible isentropic vortex column. We also compare the $\lambda_{\rho } $ and $\lambda_{2} $ structures for several numerically simulated flows, e.g., liquid jet breakup in air, compressible jet, compressible wake, and shock-turbulent boundary layer interactions. For low Mach number ($Ma<2)$ compressible flows, we find that the structures identified by $\lambda_{2} $ and $\lambda_{\rho } $ definitions are nearly identical - indicating that $\lambda_{2} $ method can still be used for low Mach number compressible flows. [Preview Abstract] |
Sunday, November 19, 2017 9:31AM - 9:44AM |
A9.00008: Combined High-Speed 3D Scalar and Velocity Reconstruction of Hairpin Vortex Daniel Sabatino, Tobias Rossmann, Xuanyu Zhu, Mary Thorsen The combination of 3D scanning stereoscopic particle image velocimetry (PIV) and 3D Planar Laser Induced Fluorescence (PLIF) is used to create high-speed three-dimensional reconstructions of the scalar and velocity fields of a developing hairpin vortex. The complete description of the regenerating hairpin vortex is needed as transitional boundary layers and turbulent spots are both comprised of and influenced by these vortices. A new high-speed, high power, laser-based imaging system is used which enables both high-speed 3D scanning stereo PIV and PLIF measurements. The experimental system uses a 250 Hz scanning mirror, two high-speed cameras with a 10 kHz frame rate, and a 40 kHz pulsed laser. Individual stereoscopic PIV images and scalar PLIF images are then reconstructed into time-resolved volumetric velocity and scalar data. The results from the volumetric velocity and scalar fields are compared to previous low-speed tomographic PIV data and scalar visualizations to determine the accuracy and fidelity of the high-speed diagnostics. Comparisons between the velocity and scalar field during hairpin development and regeneration are also discussed. [Preview Abstract] |
Sunday, November 19, 2017 9:44AM - 9:57AM |
A9.00009: Vortex scaling ranges in two-dimensional turbulence Helen Burgess, Richard Scott, David Dritschel We introduce a scaling theory for vortices in the forced inverse energy cascade of 2D turbulence. Far-from-equilibrium systems generically exhibit multiple scaling regimes associated with transport of conserved quantities. Motivated by this observation, we model a three-part time-evolving vortex number density distribution, $n(A)\sim t^{\alpha_i} A^{-r_i}, \ i \in 1,2,3$, conserving the first three moments of $\overline{\omega_\text{v}^2}n(A)$ in three distinct scaling ranges. Here $\overline{\omega_\text{v}^2}$ is the `vortex intensity', or mean square vorticity evaluated over vortices, and areas $A$ are intense regions of vorticity bounded by vorticity isolines. We predict $\alpha_i$ and $r_i$ by enforcing conservation in `comoving intervals', whose endpoints evolve at the vortex growth rate; this amounts to assuming invariance under the dilatation of flow features associated with the inverse cascade, and that vortex area growth is the appropriate measure of dilatation in all scaling ranges. High resolution numerical simulations verify the predictions, which are insensitive to the vorticity threshold used to isolate the areas. Similar concepts can be applied to model vortices in decaying 2D turbulence, pointing toward a unified description of vortices in both systems. [Preview Abstract] |
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