Bulletin of the American Physical Society
72nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 64, Number 13
Saturday–Tuesday, November 23–26, 2019; Seattle, Washington
Session L12: Vortex Dynamics and Vortex Flow: Instability |
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Chair: Eckart Meiburg, UCSB Room: 303 |
Monday, November 25, 2019 1:45PM - 1:58PM |
L12.00001: Turbulence generation through an iterative cascade of the elliptical instability Ryan McKeown, Rodolfo Ostilla-Monico, Alain Pumir, Michael Brenner, Shmuel Rubinstein We demonstrate the existence of a novel mechanism in which two counter-rotating vortices violently collide and break down, leading to the rapid development of a turbulent energy cascade mediated by iterations of the elliptical instability. We probe the full 3D dynamics of this breakdown by conducting both experimental visualizations of colliding vortex rings and numerical simulations of colliding vortex rings and vortex tubes. We observe how the onset of the elliptical instability causes the vortex cores to develop antisymmetric perturbations, which give rise to an ordered array of secondary vortex filaments, perpendicular to the original cores. Adjacent secondary filaments counter-rotate and interact with each other in the same manner as the original configuration. In the high-Reynolds number limit, we observe another iteration of this instability, whereby a new generation of tertiary filaments forms perpendicular to the interacting secondary filaments. The energy spectrum of this turbulent breakdown exhibits $ \sim k^{-5/3}$ scaling, a hallmark of homogeneous isotropic turbulence. We find that the elliptical instability must play a major role in the formation and sustenance of turbulent flows by providing a means through which energy is conveyed down to dissipative scales. [Preview Abstract] |
Monday, November 25, 2019 1:58PM - 2:11PM |
L12.00002: Vortical structures of an axisymmetrically oscillating self-excited jet subjected to transverse acoustic forcing Abhijit Kumar Kushwaha, Nicholas Worth, James R. Dawson, Larry K.B. Li We experimentally examine the vortical structures in the near-field region of an axisymmetrically oscillating self-excited low-density jet subjected to axial and transverse acoustic forcing. We apply the forcing at frequencies around the global frequency of the jet and measure its response via time-resolved stereoscopic particle image velocimetry. We find that, when forced at amplitudes sufficient for synchronization, the jet exhibits two distinct types of coherent structures: (i) in-phase roll-up of shear layers when the forcing is axial and (ii) anti-phase roll-up of shear layers when the forcing is transverse. We find that the latter type coincides with a suppression of the self-excited global mode via asynchronous quenching. Using proper orthogonal decomposition, we extract the dominant modes of the jet, resolving the flow structures associated with acoustic and vortical disturbances. As well as providing new insight into the way external acoustic oscillations interact with self-excited hydrodynamic oscillations, this study clarifies the role of symmetry breaking in suppressing global instability in axisymmetrically oscillating self-excited jets. [Preview Abstract] |
Monday, November 25, 2019 2:11PM - 2:24PM |
L12.00003: Topology and dissipation during vortex reconnection Robert M. Kerr The evolution of the vortical,topological and geometric properties of several configurations of vortices are compared. Trefoil vortex knots, coiled rings, anti-parallel perturbed vortices and colliding rings and one goal is to identify what the influence twist, writhe, linking numbers and helicities have upon the generation, or suppression, of energy dissipation. The focus will be upon the latest anti-parallel vortices reconnection calcualtions for which the growth of the enstrophy $Z$, the volume-integrated vorticity squared, is consistent with $\nu$-independent energy dissipation $\Delta E_\epsilon=\int_0^{t_\epsilon} \epsilon\,dt$, $\epsilon=\nu Z$ when the Reynolds number is high enough and the domain is large enough. This is consistent with the $\nu$-independent growth of $\epsilon$ for trefoil vortices (JFM 839, R2, 2018) and the type of reconnection structures observed when vortex rings collide (McKeown et al. PR Fluids 3, 124702, 2018). However, the $Z\sim (T_c(\nu)-t)^{-2}$ (or linear B_\nu(t)=(\sqrt{\nu}Z)^{-1/2}$) regime seen for trefoils and nested coiled rings (JFM 854, R2, 2018) is not observed. Could the geometric numbers and helicity be why? The helicity of anti-parallel vortices is identically zero, while the others' topological helicity=twist+writhe is large. [Preview Abstract] |
Monday, November 25, 2019 2:24PM - 2:37PM |
L12.00004: Flow-Induced Flapping Foil Instability. Jiaqi Mai, Paul F. Fischer, Arne J. Pearlstein We have conducted a computational investigation of two-dimensional self-excited flapping-foil instability in the channel formed by two parallel plates, up to Reynolds numbers (based on average velocity and plate separation) of 400, and the effects on heat transfer. Our approach, for a massless foil, spatially discretizes the incompressible Navier-Stokes equations by a spectral-element method, while the dynamical equation describing foil deformation is discretized by a p-type finite element method. The spectral-element mesh for fluid temporally moves, based on an arbitrary Lagrangian-Eulerian (ALE) formulation, so that zero-thickness foil is always attached to the mesh and the no-slip condition is satisfied. Nonlinear terms in the incompressible Navier-Stokes equations are advanced explicitly in time, while linear terms are advanced implicitly. The structural equations are advanced in a weakly coupled sense, consistent with semi-implicit temporal discretization of Navier-Stokes, and the ALE moving-mesh strategy. We update the flow from Navier-Stokes, with a prescribed zero relative velocity on the foil, by superposing a series of Stokes solutions, each representing unit acceleration for one discretized degree of freedom of the foil, and weighted to satisfy the structural equation. This approach efficiently avoids the numerical instability of traditional partitioned fluid-structure interaction algorithms in the zero-mass case. [Preview Abstract] |
Monday, November 25, 2019 2:37PM - 2:50PM |
L12.00005: Coupling of vortex breakdown and stability in a vortex T-mixer flow San To Chan, Jesse Ault, Simon Haward, Eckart Meiburg, Amy Shen We use microfluidic experiments and numerical simulations to study the flow in a vortex T-mixer: a T-shaped channel with staggered, offset inlets. The vortex T-mixer flow is characterized by a single dominant vortex, the stability of which is closely coupled to the appearance of vortex breakdown. Specifically, at a flow Reynolds number of Re $\sim$ 90, a first vortex breakdown region appears in the steady state solution, rendering the vortex pulsatively unstable. A second vortex breakdown region appears at Re $\sim$ 120, which restabilizes the vortex. Finally, a third vortex breakdown region appears at Re $\sim$ 180, which renders the vortex helically unstable. Thus, a counter-intuitive flow regime exists for the vortex T-mixer in which increasing the flow Reynolds number has a stabilizing effect on the steady state flow. Our study showcases microfluidics as an effective new tool to study vortex dynamics and provides experimental and numerical evidence of the close coupling between vortex breakdown and flow stability. [Preview Abstract] |
Monday, November 25, 2019 2:50PM - 3:03PM |
L12.00006: Influence of bottom topography on vortex stability Bowen Zhao, Emma Chieusse-Gerard, Glenn Flierl The effects of topography on the linear stability of both barotropic vortices and two-layer, baroclinic vortices are examined by considering cylindrical topography and vortices with stepwise relative vorticity profiles in the quasi-geostrophic approximation. Four vortex configurations are considered, classified by the number of relative vorticity steps in the horizontal and the number of layers in the vertical. In the barotropic calculation, the vortex is destabilized by topography having an oppositely signed potential vorticity jump while stabilized by topography of same-signed jump, i.e. anticyclones are destabilized by seamounts while stabilized by depressions. Further, topography of appropriate sign and magnitude can excite a mode-1 instability for a two-step vortex, especially relevant for topographic encounters of an otherwise stable vortex. The baroclinic calculation is in general consistent with the barotropic calculation except that the growth rate weakens and, for a two-step vortex, becomes less sensitive to topography (sign and magnitude) as baroclinicity increases. The smaller growth rate for a baroclinic vortex is consistent with previous findings that vortices with sufficient baroclinic structure could cross the topography relatively easily. [Preview Abstract] |
Monday, November 25, 2019 3:03PM - 3:16PM |
L12.00007: Analysis of the transition between Kelvin's equilibria using proper orthogonal decomposition Mira Kim, Hamid Ait Abderrahmane, Hoi Dick Ng, Georgios Vatistas The stirring flow driven by a rotating disk of a shallow water layer confined in a cylindrical bucket is revisited. The formation of a system of two and three satellite vortices, nested within slightly elliptical and triangular paraboloid free surface, orbiting around the center of the disk, is observed. At critical disk speeds transitions between these two systems of satellite vortices occur. These transitions were imaged and the velocity fields at the free surface of the shallow water were obtained via particle image velocimetry (PIV) measurement. The nucleation or the inhalation of the satellite vortex during the two transitions is discussed in relation with the eigenmodes of the vortex-patterns. [Preview Abstract] |
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