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 D12: Vortex II |
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Chair: Shilpa Khatri, University of North Carolina Room: 26B |
Sunday, November 18, 2012 2:15PM - 2:28PM |
D12.00001: Vortex roll-up in a stratified fluid Surupa Shaw, John McHugh Recent simulations of a vortex pair in a stratified fluid show that in some parameter regions the vortices disintegrate into internal waves. The kinetic energy loss for the vortex pair in this regime is remarkably fast, essentially annihilating the coherent vortex pair before any propagation. Hence the wave making occurs very early in the process. If the vortex pair is created by flow past a wing, then this wavemaking will occur mostly during the roll-up process of the trailing vorticity, and this is considered here. Results are obtained numerically using a spectral method, the flow is treated as Boussinesq and viscous, and the initial conditions are approximately the flow due to a line vortex. The results show that wavemaking is important over a much wider parameter range when the vorticity rolls-up in a stratified flow compared to previous simulation results. However for very strong vortex flows, there is no significant wavemaking, and the distributed vorticity very quickly rolls-up into a vortex pair. [Preview Abstract] |
Sunday, November 18, 2012 2:28PM - 2:41PM |
D12.00002: Experiments and numerical simulations of dense-core vortex rings in a sharply stratified environment Richard McLaughlin, Roberto Camassa, Shilpa Khatri, Keith Mertens, Claudio Viotti Ambient stratification strongly influences the mixing and dispersion properties of particle dynamics. Much insight can be gained by studying the simplified setup of vortex ring dynamics. We present three dimensional direct numerical simulations of the dynamics for a vortex ring settling in sharply stratified miscible ambient fluids for two layer configurations. These simulations are compared with experiments conducted in the UNC Joint Fluids Lab. The core fluid of the vortex rings has density higher than both the top and bottom layers of the ambient fluid, and is fully miscible in both layers. This setup results in a rich parameter space which we partially present here. In particular, a critical (bifurcation) phenomenon is identified which distinguishes long-time behavior of the falling vortex ring. The ring either fully traps at the ambient density layer, or continues through the layer in its downward motion. This critical behavior is set by initial conditions (e.g., size and speed of the vortex ring, initial distance to the layer, etc.). Detailed comparisons between experiments and simulations for density, velocity, and vorticity fields will be discussed. [Preview Abstract] |
Sunday, November 18, 2012 2:41PM - 2:54PM |
D12.00003: Structure of a vorticity patch bounded by a vortex sheet in strain Daniel Freilich, Stefan Llewellyn Smith Llewellyn Smith and Crowdy[\emph{J.\ Fluid Mech}.\ \textbf{691} (2012)] studied the shape and stability of a constant pressure region bounded by a jump in the Bernoulli constnat, i.\ e.\ a vortex sheet, in an ambient irrotational straining field. We extend this work to the case of a two-dimensional vortex sheet bounding a uniform voricity patch, again in an ambient irrotational straining field. We obtain the relation between the two governing nondimensional parameters relating the strengths of the straining field, vortex sheet and vorticity in the patch, and examine the shape of the resulting vortex. We also investigate the lowest order correction for the shape of the vortex when the straining field is weak. [Preview Abstract] |
Sunday, November 18, 2012 2:54PM - 3:07PM |
D12.00004: ABSTRACT WITHDRAWN |
Sunday, November 18, 2012 3:07PM - 3:20PM |
D12.00005: On the Anti-Symmetric Modes of Crow Instability by a General Instability Analysis Method Zhongquan Charlie Zheng, Jay Hardin The sinusoidal instability of a counter-rotation vortex pair has been investigated in Crow's seminal work (Crow, 1970). The anti-symmetric modes of instability were considered weak interaction modes by Crow, although they are the most amplified modes, according to Fig.11 in his paper. The weak interaction instability modes are those disturbances that are near the zero-self-induction and in the high wave-number range. However, later Saffman (1992) stated that all the anti-symmetric modes were stable. In this paper, the disturbance matrix is investigated. By looking at the eigenvalues and eigenvectors of the growth matrix, the symmetric and anti-symmetric modes of Crow's instability are recovered. Furthermore, by using a general instability analysis method of Farrell and Ioannou (1996), the upper bounds of the instability can be obtained, which again proves that the anti-symmetric modes are more amplified. These anti-symmetric modes can occur in both the long-wave modes and short-wave modes. [Preview Abstract] |
Sunday, November 18, 2012 3:20PM - 3:33PM |
D12.00006: Lifetime and layering of vortices in rotating stratified fluids Oriane Aubert, Micha\"el Le Bars, Patrice Le Gal Ocean and atmosphere are natural stratified fluid layers influenced by the rotation of the planet through the Coriolis force, where it is common to observe long-lived anticyclonic vortices sometimes surrounded by layers of constant density as the ocean Meddies. In the continuity of the experiments of Griffiths \& Linden (1981) and Hedstrom \& Armi (1988), we reproduce a rotating and linearly stratified layer in a tank where freely-decaying or sustained laboratory anticyclonic vortices are created via a short or continuous injection of isodense fluid. We quantify their long term evolution using PIV measurements. The Rossby number $Ro$ of the freely-decaying vortices decreases in time, which is theoretically described by the energy conservation equations applied to a gaussian model that fits both laboratory and oceanic vortices. Using this theory and numerical simulations, we investigate the respective roles of rotation and stratification to explain the longevity of the vortices. $Ro$ for the sustained vortices remains large and allows for the formation of layers above and below the vortices, following the double-diffusive instability of McIntyre (1970). Typical length and time scales of the instability are well described by a linear stability analysis based on our gaussian model. [Preview Abstract] |
Sunday, November 18, 2012 3:33PM - 3:46PM |
D12.00007: A bypass transition in the Lamb-Oseen vortex Luigi Bisanti, Pierre Brancher, Christophe Airiau Transient energy growth in the short-time linear dynamics of a Lamb-Oseen monopole is a potential mechanism for nonlinear bypass transition, a phenomenon already observed in both experiments and numerical simulations. In the present study, we investigate this scenario by means of a nonlinear optimal perturbation approach, i.e. by looking for the initial perturbation whose evolution satisfies the fully nonlinear Navier-Stokes equations and maximizes the energy gain at a given time horizon. Preliminary two-dimensional results show that, for small initial amplitudes, the optimal perturbation and growth mechanisms observed in the linear regime are recovered. More particularly, the time evolution of the $m=2$ optimal perturbation leads to an elliptical core deformation of the monopole, which suggests a potential bypass scenario driven by the non-linear dynamics. This is confirmed by computations for larger initial perturbation amplitudes: the optimal perturbation is similar to that of the linear regime but a subcritical bifurcation to a quasi-steady, high-energy, rotating tripole is observed. [Preview Abstract] |
Sunday, November 18, 2012 3:46PM - 3:59PM |
D12.00008: Formation of type II vortex streets Ildoo Kim, X.L. Wu In experiments in 2D soap film, we observe two kinds of vortex streets. The ``type I'' vortex street is stable and its K\'{a}rm\'{a}n ratio (the ratio of the transverse spacing to the longitudinal spacing of constituent vortices) is between 0.3 and 0.5. In contrast, the ``type II'' vortex street is characterized by its meta-stability and a much higher K\'{a}rm\'{a}n ratio, measured between 0.5 and 0.7. We studied the condition of formation of the type II vortex street by independently controlling two length scales of the system - the head-on width of the obstacle $W$ and the thickness of the boundary layer $\delta$ before detachment. Our experiment suggests that the vortex street is type II when $\delta/W<0.4$. The type II vortex street eventually evolves into the type I at downstream. The lifetime of this meta-stable configuration is strongly affected by the thickness $\delta$ of the boundary layer. [Preview Abstract] |
Sunday, November 18, 2012 3:59PM - 4:12PM |
D12.00009: ABSTRACT WITHDRAWN |
Sunday, November 18, 2012 4:12PM - 4:25PM |
D12.00010: Vortex Dynamics in High Reynolds number, Acoustically Forced, Reacting Wakes near the Global Stability Boundary Benjamin Emerson, Kelvin Murphy, Tim Lieuwen This abstract discusses results from a set of PIV experiments involving longitudinally acoustically forced, bluff body stabilized flames. It is well known that wakes stabilizing high density ratio flames are convectively unstable and thus are more receptive to acoustic forcing, while low density ratio wakes are globally unstable and thus tend to oscillate at a global mode frequency. When the wake is forced near its natural frequency, its peak response may shift to (or towards) the forcing frequency, a phenomenon known as lock-in. These experiments show that the longitudinal forcing launches a pair of symmetrically shed vortices from the bluff body, in contrast with the wakes natural asymmetry. As the lock-in phenomenon is approached, the symmetrically stimulated vortices convect downstream initially in their varicose configuration, but then stagger until they are arranged in a sinuous configuration. The axial position at which this staggering occurs is a strong function of how close the forcing frequency is to the natural frequency, and the amplitude of the forcing. This effect is made evident by the spatial distribution of vortical fluctuations, by ensemble averaged vorticity contours, and by the cross spectrum of the fluid dynamics on either side of the flow centerline. This staggering process, and the position at which it occurs, has important implications on the thermoacoustics of bluff body stabilized flames, as it governs the dynamics of the heat release and its receptivity to acoustic forcing. [Preview Abstract] |
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