Bulletin of the American Physical Society
69th Annual Meeting of the APS Division of Fluid Dynamics
Volume 61, Number 20
Sunday–Tuesday, November 20–22, 2016; Portland, Oregon
Session E3: Vortex Dynamics: Theory |
Hide Abstracts |
Chair: Kamran Mohseni, University of Florida Room: B110-111 |
Sunday, November 20, 2016 5:37PM - 5:50PM |
E3.00001: Sources of vorticity at interface curvature singularities and the triple contact point Peter Zhang, Kamran Mohseni In our recent two-phase experiments [DeVoria \& Mohseni, Phys. Fluids, 27(1), 2015], high concentrations of positive and negative vorticity have been observed near the moving contact line. These distributions suggest that the moving contact line, characterized by singular interface curvature, may be a unique source of vorticity. Motivated by this possibility, we conduct an analytic investigation of vorticity generation near sharp corners. To model the problem, we assume that the fluid is governed by the Stokes flow equations whose solutions can be found analytically. The general solution is composed of an exterior and interior multipole expansion, indicating sources of vorticity at or far from the corner respectively. A vorticity monopole, characterized by constant vorticity generation from the corner singularity, is observed for corner flows with logarithmic interface normal velocity only. A vorticity dipole and quadrupole are identified as the vorticity distribution for a moving contact line and interface cusp respectively. Using the analytic solution, exact relations for the vorticity multipole strengths and orientations are derived. A comparison of the analytic model with experimental measurements and numerical simulations show agreement in the vicinity of the corner. [Preview Abstract] |
Sunday, November 20, 2016 5:50PM - 6:03PM |
E3.00002: The hydrodynamic vortex: an exactly solvable black hole analogue Nail Ussembayev We consider the Cauchy problem for the Klein-Gordon equation on an effective Lorentzian manifold describing the sound propagation on a background flow undergoing a subsonic-supersonic transition. For the hydrodynamic vortex model, a particular case of a draining bathtub geometry with non-zero circulation and no draining, we derive an exact solution and discuss its properties. [Preview Abstract] |
Sunday, November 20, 2016 6:03PM - 6:16PM |
E3.00003: The boundary-constraint method for constructing vortex-surface fields Shiying Xiong, Yue Yang We develop a boundary-constraint method for constructing the vortex-surface field (VSF) in a three-dimensional fluid velocity field. The isosurface of VSF is a vortex surface consisting of vortex lines, which can be used to identify and track the evolution of vortical structures in a Lagrangian sense. The evolution equation with pseudo-time is solved under the boundary constraint of VSF to obtain an approximate solution of VSF. Using the boundary-constraint method, we construct the VSFs in Taylor-Green flow and transitional channel flow. The uniqueness of VSF are demonstrated with different initial conditions, and the consistency of this boundary-constraint method and the previous two-time approach for constructing VSF is discussed. In addition, the convergence error in the calculation of VSF is analyzed. [Preview Abstract] |
Sunday, November 20, 2016 6:16PM - 6:29PM |
E3.00004: Extreme Growth of Enstrophy on 2D Bounded Domains Bartosz Protas, Adam Sliwiak We study the vortex states responsible for the largest instantaneous growth of enstrophy possible in viscous incompressible flow on 2D bounded domain. The goal is to compare these results with estimates obtained using mathematical analysis. This problem is closely related to analogous questions recently considered in the periodic setting on 1D, 2D and 3D domains. In addition to systematically characterizing the most extreme behavior, these problems are also closely related to the open question of the finite-time singularity formation in the 3D Navier-Stokes system. We demonstrate how such extreme vortex states can be found as solutions of constrained variational optimization problems which in the limit of small enstrophy reduce to eigenvalue problems. Computational results will be presented for circular and square domains emphasizing the effect of geometric singularities (corners of the domain) on the structure of the extreme vortex states. [Preview Abstract] |
Sunday, November 20, 2016 6:29PM - 6:42PM |
E3.00005: Maximum Production of Enstrophy in Swirling Viscous Flows Diego Ayala, Charles Doering We study a family of axisymmetric vector fields that maximize the instantaneous production of enstrophy in 3-dimensional (3D) incompressible viscous flows. These vector fields are parametrized by their energy $\mathcal{K}$, enstrophy $\mathcal{E}$ and helicity $\mathcal{H}$, and are obtained as the solution of suitable constrained optimization problems. The imposed symmetry is justified by the results reported in the seminal work of Doering \& Lu (2008), recently confirmed independently by Ayala \& Protas (2016), where highly-localized pairs of colliding vortex rings are found to be optimal for enstrophy production. The connection between these optimal axisymmetric fields and the ``blow-up'' problem in the 3D Navier-Stokes equation is discussed. [Preview Abstract] |
Sunday, November 20, 2016 6:42PM - 6:55PM |
E3.00006: The critical swirl of a subsonic compressible swirling flow of a perfect gas in a finite-length straight circular pipe Harry Lee, Zvi Rusak, Shixiao Wang Functional analysis techniques are used to rigorously determine the range of flow Mach number $Ma_0$ for the existence of the critical swirl ratio $\omega_1$ for exchange of stability of a base columnar compressible swirling flow of a perfect gas in a finite-length straight circular pipe. For swirling flows with a monotonic circulation profile, it is first established that $\omega_1$ definitely exists in the range
$0< Ma_0 <2\sqrt{\gamma-1}/\gamma$, where $\gamma>1$ is the ratio of specific heats of the gas. Then, the existence of a limit Mach number $Ma_{0l}$ between $2\sqrt{\gamma-1}/\gamma$ and $1$ is proven for a subclass of swirling flows; i.e. $\omega_1$ does not exist and the flow is stable for all swirl level when $Ma_{0l}< Ma_0 <1$. For example, $0.903 |
Follow Us |
Engage
Become an APS Member |
My APS
Renew Membership |
Information for |
About APSThe American Physical Society (APS) is a non-profit membership organization working to advance the knowledge of physics. |
© 2024 American Physical Society
| All rights reserved | Terms of Use
| Contact Us
Headquarters
1 Physics Ellipse, College Park, MD 20740-3844
(301) 209-3200
Editorial Office
100 Motor Pkwy, Suite 110, Hauppauge, NY 11788
(631) 591-4000
Office of Public Affairs
529 14th St NW, Suite 1050, Washington, D.C. 20045-2001
(202) 662-8700