Bulletin of the American Physical Society
65th Annual Meeting of the APS Division of Fluid Dynamics
Volume 57, Number 17
Sunday–Tuesday, November 18–20, 2012; San Diego, California
Session G12: Vortex IV |
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Chair: Peter Hamlington, University of Colorado Room: 26B |
Monday, November 19, 2012 8:00AM - 8:13AM |
G12.00001: Listening to the horseshoe vortex system: interpretation of turbulent coherent structures by Parameter Mapping Sonification Juan-Pablo Caceres, Cristian Escauriaza The adverse pressure gradient induced by a surface-mounted obstacle in a turbulent boundary layer causes the formation the dynamically rich horseshoe vortex system around the body. Recent studies have identified the complex mechanisms responsible for the dynamics of the vortices and the emergence of bimodal histograms of velocity fluctuations in the junction region. To understand the dynamic relation of the multiple vortices, we convert streamwise velocity time-series at the symmetry plane into sound by Parameter Mapping Sonification, to make emerge aspects of the rich-dynamics of the turbulent coherent structures in the vortex system that may not have been uncovered by traditional methods. Through this development we provide insights on the analysis of turbulent flows dominated by the quasi-periodic interaction of large-scale coherent vortices. [Preview Abstract] |
Monday, November 19, 2012 8:13AM - 8:26AM |
G12.00002: A flow visualization and volumetric particle-image velocimetry study on low Reynolds number inclined rectangular jets Yong Chuan Khoo, Tze How New, Wing Lai Flow visualizations and three-dimensional volumetric particle image velocimetry measurements were performed on Re=2,500 jets produced by aspect-ratio of three rectangular nozzles inclined at 60$^{\circ}$ along their major and minor-planes. Results show that persistently inclined azimuthal ring vortices are formed, regardless of the exact incline-plane used. When the nozzle is inclined along its major-plane, these ring vortices undergo rapid realignments which reduce their inclination and coherence. In contrast, they retain their inclination for a significantly further downstream distance when the nozzle is inclined along its minor-plane instead. As such, gross large-scale vortex structures and behaviour are relatively similar to those observed for inclined elliptic nozzles previously. In contrast to inclined elliptic nozzles with no corners, small-scale streamwise vortex structures are produced by the rectangular nozzle sharp corners which hasten the onset of large-scale vortical changes for a faster transition to flow incoherence. These observations indicate that at the present working conditions, inclined jet behaviour is more sensitive towards the redistribution of jet circulation caused by the nozzle inclination, rather than variations between different nozzle base geometries. [Preview Abstract] |
Monday, November 19, 2012 8:26AM - 8:39AM |
G12.00003: Ellipsoidal vortices beyond the quasi-geostrophic approximation Yue-Kin Tsang, David Dritschel, Jean Reinard As a model of geophysical vortices, we study numerically the behavior of an ellipsoidal volume of uniform potential vorticity in a non-hydrostatic, rotating stratified flow. Previous studies on ellipsoidal vortices mainly focus on the quasi-geostrophic regime. Here, we aim to determine the effects of ageostrophy on the stability, evolution and the final fate of the vortices. Cyclonic and anti-cyclonic vortices of various aspect ratios are investigated. Generally, cyclonic vortices with roughly circular cross section tend to be more stable. In the cases when the vortices become unstable, a wide range of nonlinear evolution is observed including tumbling, shape vacillation, splitting and filaments shedding. Diagnostics concerning the vortex rotation rate and the degree of ``imbalance,'' which quantifies the amount of internal gravity waves emission, will be presented. [Preview Abstract] |
Monday, November 19, 2012 8:39AM - 8:52AM |
G12.00004: On Optimal Vortex Structures for Palinstrophy Generation Diego Ayala, Bartosz Protas We are interested in identifying the vortex structures which lead to the largest growth of palinstrophy $\mathcal{P}$ in flows governed by the 2D Navier--Stokes equation in a periodic domain. This problem is a 2D counterpart of the problem concerning the maximal production of enstrophy $\mathcal{E}$ in 3D Navier--Stokes flows which is inherently related to the question of finite--time singularity formation. We investigate the sharpness of the following analytic estimates $$ \frac{d\mathcal{P}}{dt}\sim\mathcal{P}^{2}\quad\mbox{and}\quad\max_{t>0}\mathcal{P}(t)\sim\mathcal{P}(0)^{2}\quad\mbox{as}\quad\mathcal{P}\to\infty $$ by studying suitable optimization problems. These problems are solved for different values of the palinstrophy using modern methods of PDE--constrained optimization combined with DNS. In regard to the instantaneous problem, we discover two families of maximizing fields characterized by distinct properties. We also present evidence that the maximum growth of $\frac{d\mathcal{P}}{dt}$ with $\mathcal{P}$ is in fact weaker than suggested by the analytic estimate. [Preview Abstract] |
Monday, November 19, 2012 8:52AM - 9:05AM |
G12.00005: A highly adaptive three dimensional hybrid vortex method for inviscid flows Dan Lucas, David G. Dritschel Motivated by outstanding problems surrounding vortex stretching (e.g. explosive vorticity growth, equation regularity and associated nonlinear depletion), a new hybrid vortex method for inviscid, three-dimensional, incompressible flows is presented. Special emphasis on spatial adaptivity is given to resolve as broad a range of scales as possible in a completely self-similar fashion. We discretise vorticity in Lagrangian filaments (space curves) and compute velocity on an adapted finite-volume grid. This allows for a two-fold adaptivity strategy. First, although naturally spatially adaptive by definition, the vorticity filaments undergo ``renoding''; nodes are redistributed along the filaments to concentrate their density in regions of high curvature. Secondly the Eulerian mesh is adapted to follow high strain by determining resolution by way of local filament dimensions. These features allow vortex stretching and folding to be resolved in a completely automatic and self-similar way, in addition the filaments present themselves as a candidate for novel flow diagnostics. Validation of the method is demonstrated via relatively recently discovered helical vortex equilibria (Lucas \& Dritschel 2009). [Preview Abstract] |
Monday, November 19, 2012 9:05AM - 9:18AM |
G12.00006: 2D FTLE in 3D Flows: The accuracy of using two-dimensional data for Lagrangian analysis in a three-dimensional turbulent channel simulation Matthew Rockwood, Melissa Green In experimental, three-dimensional vortex-dominated flows, common particle image velocimetry (PIV) data is often collected in only the plane of interest due to equipment constraints. For flows with significant out of plane velocities or velocity gradients, this can create large discrepancies in Lagrangian analyses that require accurate particle trajectories. A Finite Time Lyapunov Exponent (FTLE) analysis is one such example, and has been shown to be very powerful at examining vortex dynamics and interactions in a variety of aperiodic flows. In this work, FTLE analysis of a turbulent channel simulation was conducted using both full three-dimensional velocity data and modified planar data extracted from the same computational domain. When the out of plane velocity component is neglected the difference in FTLE fields is non-trivial. A quantitative comparison and computation of error is presented for several planes across the width of the channel to determine the efficacy of using 2D analyses on the inherently 3D flows. [Preview Abstract] |
Monday, November 19, 2012 9:18AM - 9:31AM |
G12.00007: Numerical simulation of the velocity field and vorticity in a flow occurring in a channel and an open domain with periodic forcing Erick Lopez-Sanchez, Gerardo Ruiz-Chavarria The system under study is a flow with periodic forcing in a channel that flows out toward an open domain. At the channel exit a pair of vortices is formed for each period. Using a pseudo-spectral method based on Chebyshev polynomials, the Navier-Stokes and continuity equations are solved numerically in the stream function-vorticity formulation (2D). The equations are integrated during several periods and for different values of Reynolds and Strouhal numbers. We found that the dipoles persist for more than one period and that their evolution depends strongly on the Strouhal number as predicted in previous works (e. g. Dynamics of Atmospheres and Oceans, 37 (2003) 223-244) but a rich dynamics emerges when interaction among vortices is taken account. For instance coalescence of vortices of the same sign can be observed. Besides this case, other two possibilities can be envisaged, namely, the dipoles travel a long distance if compared with the channel width and escapes or the dipoles fails to form completely and return to the channel when period is so short. Otherwise, numerical simulation shows the appearance of a sinusoidal instability which is a mechanism for the destruction of the vortices. Comparison with experimental and observational data is performed giving a good agreement. [Preview Abstract] |
Monday, November 19, 2012 9:31AM - 9:44AM |
G12.00008: A Bathtub Vortex under the Influence of a Taylor Column in a Rotating Tank Shih-Lin Huang, Yin-Chung Chen, Zi-Ya Li, Chin-Chou Chu, Chien C. Chang Numerical simulations and laboratory experiments were conducted to investigate a bathtub vortex under the influence of a Taylor column in a rotating tank. A central drain hole is placed at the bottom of the tank and a top-down cylinder is suspended from the rigid lid. We examine the effects of the Rossby number, \textit{Ro} and the Ekman number, \textit{Ek}. Steady-state solutions are shown to have good agreements with flow visualizations and PTV measurements. It is found that at \textit{Ro}$\sim $10$^{-2}$, a bottom Ekman pumping forms a classic one-celled structure for the case of no suspended cylinder $h/H$=0, while for various $h/H\ne $0, the strong interaction of the bathtub vortex and Taylor column results in a two-celled structure with an inner Ekman pumping and an outer Taylor column induced upwelling. In $h/H\ne $0, the Taylor wall separates the vortex into an inner and an outer region, but allows the outer fluid to flow into the inner region through a top and a bottom gap which can be classified into two and three flow paths, respectively. Moreover, the individual flow rate of each path and the weaker influence of the Taylor column at \textit{Ro}$\sim $1 and $\sim $10$^{2}$ are also discussed. Finally, we observe that the vorticity strength of the vortex exhibits the relationship with a dimensionless group$\sqrt {fQ/gH^2(1-h/H)} $. [Preview Abstract] |
Monday, November 19, 2012 9:44AM - 9:57AM |
G12.00009: Unbounded Immersed Interface solver, also for use in Vortex Particle-Mesh methods Yves Marichal, Philippe Chatelain, Gregoire Winckelmans We present a new and efficient algorithm to solve the 2-D Poisson equation in unbounded domain and with complex inner boundaries. It is based on an efficient combination of two components: the Immersed Interface method to enforce the boundary condition on each inner boundary (here using solely 1-D stencil corrections) and the James-Lackner algorithm to compute the outer boundary condition consistent with the unbounded domain solution. The algorithm is here implemented using second order finite differences and is particularized to the computation of potential flow past solid bodies. It is validated, by means of grid convergence studies, on the flow past multiple bodies (some also with circulation). The results confirm the second order accuracy everywhere. The algorithm is self consistent as ``all is done on the grid'' (thus without using a Vortex Panel boundary element method in addition to the grid). The next aim of this work is then to integrate this algorithm in the Vortex Particle-Mesh (VPM) method for the computation of unsteady viscous flows, with boundary layers, detached shear layers and wakes. Preliminary results of the combined methods will also be presented. [Preview Abstract] |
Monday, November 19, 2012 9:57AM - 10:10AM |
G12.00010: Buoyancy-Induced Columnar Vortices Mark Simpson, Ari Glezer The formation of anchored, buoyancy-driven columnar vortices driven by the instability of a thermally stratified air layer, and sustained by entrainment of ground-heated air is investigated in a meter-scale laboratory facility. In hot-climate regions, buoyancy-driven columnar vortices (``dust devils'') spontaneously occur with core diameter of 1-50 m at the surface and heights up to one km, with considerable angular and axial momentum. Such vortices convert low-grade heat in an air layer overlying a warm surface into a flow with significant kinetic energy. The considerable kinetic energy of the vortex column cannot be explained by buoyancy alone and is a result of the production, concentration, and tilting of the horizontal vorticity produced in the air layer over the heated ground plane. The present investigation focuses on the fundamental mechanisms of the formation, evolution, and dynamics of the columnar vortex using stereo-PIV with emphasis on scaling and assessment of the available kinetic energy. It is shown that the strength and scaling of these vortices can be significantly altered through adjustments of the flow vanes and the global sensible heat absorbed by the air flow. [Preview Abstract] |
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