Bulletin of the American Physical Society
68th Annual Meeting of the APS Division of Fluid Dynamics
Volume 60, Number 21
Sunday–Tuesday, November 22–24, 2015; Boston, Massachusetts
Session G29: Nonlinear Dynamics and Waves II |
Hide Abstracts |
Chair: Emilian Parau, UEA Room: 310 |
Monday, November 23, 2015 8:00AM - 8:13AM |
G29.00001: Hydroelastic waves on elastic cells and fluid sheets Emilian Parau, Mark Blyth The deformations of an elastic cell in an uniform stream are examined numerically. Multiple solutions corresponding to steady wave modes are found. Comparisons are made with the case of a bubble with constant surface tension in an uniform stream. Related problems will be discussed, e.g. the deformation of an elastic cell in a circulatory flow and the travelling waves on fluid sheets between two elastic plates. [Preview Abstract] |
Monday, November 23, 2015 8:13AM - 8:26AM |
G29.00002: New Exact Coherent States in Channel Flow Masato Nagata, Darren Wall Three spatially periodic traveling wave exact coherent states in channel flow are presented. Two of the flows are derived by homotopy from solutions for channel flow subject to a span-wise rotation investigated by Wall \& Nagata (2013). Both these flows are asymmetric with respect to the channel center-plane, and feature streaky structures in stream-wise velocity franked by staggered vortical structures. One of these flows features two streak/vortex systems per span-wise wavelength, while the other features one such system. The third flow satisfies a half-turn rotational symmetry about a point on the channel center-plane, and turns out to be the flow from which one of the asymmetric flows bifurcates in a symmetry breaking bifurcation. One of the asymmetric flows is found to substantially reduce the value of the lowest Reynolds number at which exact solutions are known to exist down to 665. [Preview Abstract] |
Monday, November 23, 2015 8:26AM - 8:39AM |
G29.00003: Bifurcation Analysis of 1D Steady States of the B\'{e}nard Problem in the Long Wavelength Limit Chengzhe Zhou, Sandra Troian We investigate the character and stability of stationary states of the $(1+1)$D evolution equation $\partial_th+\left(h^3 h_{xxx}+h^2\partial_x\gamma\right)_x=0$ describing the motion of an interface $h(x,t)$ separating a thin warm viscous film from a thin cool inviscid layer where $\gamma=\gamma(h)$ represents the interfacial tension. The phase diagram corresponding to all positive periodic steady states (PPSS) is specified by two variables - the global extrema of the equilibrum shape and a generalized mechanical interface pressure. The analytic forms describing the PPSS shapes, the minimal period, the average height and the generalized free energy are all confirmed numerically. We find there is at most one non-trivial PPSS for specified period and volume. We also find no stable perturbed PPSS near the critical point for volume conserving perturbations of identical period. A weakly non-linear analysis about the critical point yields bifurcations of the pitchfork-type. For all non-trivial PPSS, we verify the unstable nature of the PPSS by transforming the non-normal operator (resulting from the spatially inhomogeneous PPSS) to normal form, which we then solve by finite element computations. [Preview Abstract] |
Monday, November 23, 2015 8:39AM - 8:52AM |
G29.00004: Local analysis and topological bifurcations of free surfaces Nugzar Suramlishvili, Jens Eggers The recently developed method of the local analysis\footnote{J. Eggers and M. A. Fontelos, Panoramas et Synth\`{e}ses \textbf{38}, 69 (2013).} is applied in order to determine generic singularities and topological bifurcations of free surfaces and interfaces in liquids and gases. In the presented physical examples the surface geometry is described by a family of smooth maps with the state variables and a set of control parameters. We determine the order of Taylor expansion about a point of interest defining the multiplicity of a singular germ, codimension, unfolding of singularity and bifurcation diagram. [Preview Abstract] |
Monday, November 23, 2015 8:52AM - 9:05AM |
G29.00005: bifurcations of driven cavity flow and their implications for mixing Hassan Arbabi, Igor Mezic We use the Koopman operator theory to study the sequence of bifurcations in 2D driven cavity flow. By extracting the Koopman modes (analogue to normal modes of linear-systems theory), we identify the dominant flow structures at different subranges of Reynolds number. We also use the eigenvalues of the Koopman operator to study the structural dependence of the flow on the Reynolds number and classify the asymptotic state of the unsteady flow into periodic, quasi-periodic and possibly chaotic categories. Ultimately, we perform a combined study of the Koopman modes and eigenvalues involved with each category to study the effect of each bifurcation on mixing properties of the cavity flow. [Preview Abstract] |
Monday, November 23, 2015 9:05AM - 9:18AM |
G29.00006: Koopman decompositions of periodically forced Hopf bifurcation flows and application to dynamic stall Bryan Glaz, Sophie Loire, Maria Fonoberova, Igor Mezic Periodically forced Hopf bifurcation flows, such as oscillating cylinders, can exhibit rich spectral content. Though lock-on dynamics of systems forced near resonances are well understood, the underlying chaotic or quasi-periodic dynamics when forcing away from a natural frequency are not. This behavior can be critical for systems of practical significance, such as oscillating airfoils under dynamic stall. In this study, normal form theory and spectral decompositions based on Koopman operators will be used to reveal transitions from limit cycle attractors to chaotic/quasi-periodic dynamics in the cylinder Hopf bifurcation flow. Koopman operator methods are used since each mode is associated with a single frequency which allows one to observe the evolution to more continuous spectral behavior with forcing, while approaches such as proper orthogonal decomposition may obfuscate this transition. It will be shown that projecting onto a low order subspace of Koopman modes can capture features supported by normal forms. Using this, we show a mechanism that leads to regimes in which the system seems to exhibit shear-induced chaos. The new framework is applied to dynamic stall studies to establish periodically forced Hopf bifurcation dynamics as an underlying feature. [Preview Abstract] |
Monday, November 23, 2015 9:18AM - 9:31AM |
G29.00007: Inverse energy cascade in non-local helical shell-models of turbulence De Pietro Massimo, Luca Biferale, Ganapati Sahoo, Alexei Mailybaev Following the exact decomposition in eigenstates of helicity for the Navier-Stokes equations in Fourier space we introduce a modified version of helical shell-models for turbulence with non-local triadic interactions. By using both analytical argument and numerical simulation we show that there exists a sub-class of models with elongated shell interactions that exhibits a statistically stable inverse energy cascade. Using also data from direct numerical simulations of helical Navier-Stokes equations we further support the idea that energy transfer mechanism in fully developed turbulence is the result of a strong entanglement among different triadic interactions possessing different transfer mechanisms. [Preview Abstract] |
Monday, November 23, 2015 9:31AM - 9:44AM |
G29.00008: Lagrangian coherent structures in the wake of a streamwise oscillating cylinder Neil Cagney, Stavroula Balabani Lagrangian analysis of experimental flow measurements has the ability to reveal complex coherent structures and identify phenomena that may not be apparent from standard Eulerian descriptors, such as vorticity. We measure the wake of a cylinder undergoing streamwise vortex-induced vibrations (VIVs) using Particle-Image Velocimetry, and examine the wake dynamics throughout the response regime in terms of the phase-averaged vorticity fields. The Finite-Time Lyapunov exponent (FTLE) fields are also computed in backward- and forward-time in order to identify the Lagrangian Coherent Structures. We examine four distinct wake modes that occur at various points in the response regime. The roll up of the shear layers and the vortex formation process are examined using the FTLE fields. This analysis allows the fluid-structure interaction and dynamics in the near wake to be examined in much greater detail than would be possible using the vorticity fields alone. Particular attention is paid to the symmetric vortex-shedding mode, which is characteristic to streamwise VIV; the forward-time FTLE fields show that the wake is organised into discreet ``vortex cells,'' which enclose each vortex and define its boundary. Finally, the advection of tracers in the wake is studied in order to examine how the different wake modes promote/inhibit mixing. The alternate wake modes tend to promote mixing, particularly in the second response branch, but the symmetric shedding tends to reduce the lateral mixing across the wake. [Preview Abstract] |
Monday, November 23, 2015 9:44AM - 9:57AM |
G29.00009: Chaotic advection in 2D anisotropic porous media Stephen Varghese, Michel Speetjens, Ruben Trieling, Federico Toschi Traditional methods for heat recovery from underground geothermal reservoirs employ a static system of injector-producer wells. Recent studies in literature have shown that using a well-devised pumping scheme, through actuation of multiple injector-producer wells, can dramatically enhance production rates due to the increased scalar / heat transport by means of chaotic advection. However the effect of reservoir anisotropy on kinematic mixing and heat transport is unknown and has to be incorporated and studied for practical deployment in the field. As a first step, we numerically investigate the effect of anisotropy (both magnitude and direction) on (chaotic) advection of passive tracers in a time-periodic Darcy flow within a 2D circular domain driven by periodically reoriented diametrically opposite source-sink pairs. Preliminary results indicate that anisotropy has a significant impact on the location, shape and size of coherent structures in the Poincare sections. This implies that the optimal operating parameters (well spacing, time period of well actuation) may vary strongly and must be carefully chosen so as to enhance subsurface transport. [Preview Abstract] |
Monday, November 23, 2015 9:57AM - 10:10AM |
G29.00010: Controlling the Dynamics of the Five-Mode Truncation System of the 2-d Navier-Stokes Equations Nejib Smaoui, Mohamed Zribi The dynamics and the control problem of the two dimensional (2-d) Navier-Stokes (N-S) equations with spatially periodic and temporally steady forcing is addressed. At first, the Fourier Galerkin method is applied to the 2-d N-S equations to obtain a fifth order system of nonlinear ordinary differential equations (ODE) that approximates the behavior of these equations. Simulation studies indicate that the obtained ODE system captures the behavior of the 2-d N-S equations. Then, a control law is proposed to drive the states of the ODE system to a desired fixed point. Next, a second control law is developed to synchronize two reduced order ODE models of the 2-d N-S equations having the same Reynolds number and starting from different initial conditions. Finally, simulation results are undertaken to validate the theoretical developments. [Preview Abstract] |
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