Bulletin of the American Physical Society
74th Annual Meeting of the APS Division of Fluid Dynamics
Volume 66, Number 17
Sunday–Tuesday, November 21–23, 2021; Phoenix Convention Center, Phoenix, Arizona
Session P31: Nonlinear Dynamics: General, Bifurcations, Chaos, Topology, and Transition to Turbulence |
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Chair: Piyush Grover, University of Nebraska Room: North 232 ABC |
Monday, November 22, 2021 4:05PM - 4:18PM Not Participating |
P31.00001: Persistent homology of vortex-dominated flows behind oscillating plates Marko Budisic, Melissa A Green Experimental and computational studies of vortex-dominated flows have shown that changes in the topology of vortices, that is, their structure and arrangement, correlate with the forces exerted on objects immersed in the flow. Quantifying topology using the framework of persistent homology allows for a more-explicit analysis of correlations between the topology and force measurements, both in simulated and experimental flows. Additionally, persistent homology inherently addresses the multiscale nature of determining what is meant by ``topology'' of any particular fluid flow. We demonstrate multiple approaches to computing the persistent homology of Lagrangian locations of vortices from discrete vortex models and of Eulerian vorticity fields measured in vortex-shedding experiments. In those situations when both types of data are available, we show that either approach results in equivalent topological quantifiers. Finally, we show that time-variation of persistent homology correlates with time variation of measured drag forces. These results suggest that characterizing vortex topology via persistent homology is dynamically meaningful for the study of vortex-dominated fluid flows, therefore opening avenues for the use of persistent homology as an input for optimization, machine learning, and control of fluid flows. |
Monday, November 22, 2021 4:18PM - 4:31PM |
P31.00002: Dynamics of Minimal Networks Krishna Manoj, Samadhan A Pawar, R I Sujith Dynamics of a network of oscillators has received immense attention due to its potential application in various fields such as power grids, neuronal networks, seizure dynamics, and thermoacoustic interaction in can or can-annular type gas turbines. The stability and dynamical behavior of such networks depend on various factors including the number of oscillators, coupling parameters, and topology. These factors play a vital role in networks with low number of oscillators. Here, we study the susceptibility of minimal networks of candle-flame oscillators to the variation of the aforementioned factors. We report the presence of various dynamical states such as chimera, weak chimera, clustering, amplitude death, and partial amplitude death in both open-loop and closed-loop networks of oscillators. At short separations, the oscillators exhibit in-phase synchronization or amplitude death irrespective of their topology, whereas, at larger separations, they exhibit various states with varying probabilities of occurrence. Synchronization of oscillators is found to be easier in closed-loop compared to open-loop topologies. Further, the interaction of odd number of oscillators in a ring network prefers the occurrence of symmetry-breaking states, while networks with even number of oscillators prefer synchronization states. |
Monday, November 22, 2021 4:31PM - 4:44PM |
P31.00003: Transition to turbulence in experimental small-aspect Taylor-Couette flow Wesley Toler, Christopher J Crowley, Joshua L. Pughe-Sanford, Roman O Grigoriev, Michael F Schatz Abstract: Taylor-Couette (TC) flow is a fluid system long studied for its diverse flow states and rich transitional behavior. Previous studies have examined extensively the flow behavior of large-aspect-ratio TC. However, small-aspect behavior is less well-studied, and to date the nature of the bifurcation in small-aspect counter-rotating flow at the turbulent transition is unknown. Here we consider counter-rotating Taylor-Couette (TC) flow in a small-aspect, wide-gap geometry ($\Gamma=1$, radius ratio $\eta=0.71$), and elucidate the bifurcation structure and flow states surrounding the turbulent transition as a function of both inner and outer Reynolds number. |
Monday, November 22, 2021 4:44PM - 4:57PM |
P31.00004: Exact coherent structures (ECS) and transition to turbulence in a confined active nematic Caleb Wagner, Michael M Norton, Jae Sung Park, Piyush Grover Active matter describes a class of systems that are maintained far from equilibrium by driving forces acting on the constituent particles. This internal driving allows for rich flow behavior even in the absence of external boundary driving. Confined active matter in particular exhibits rich phenomenology. Upon increasing activity from zero, such systems pass from 1) quiescent states to 2) complex, but spatiotemporally ordered states, and finally to 3) spatiotemporal chaos, i.e., 'active/mesoscale turbulence'. There is immense potential, both fundamental and practical, in developing control capabilities for steering active systems towards or away from given flow states. Here, we address this challenge for the specific case of active nematic channel flow. We take a deterministic dynamical systems approach, beginning with the corresponding set of nematohydrodynamic PDEs. The infinite-dimensional phase space of all possible flow configurations is populated by Exact Coherent Structures (ECS), which are exact solutions of the physical dynamics with distinct and regular spatiotemporal structure; examples include unstable equilibria, periodic orbits, and traveling waves. The ECSs are connected by dynamical pathways called invariant manifolds. Our main hypothesis is that active/mesoscale turbulence corresponds to a trajectory meandering in this phase space, transitioning between neighborhoods of the ECSs by traveling on the invariant manifolds. Similar approaches have been successful in characterizing high Reynolds number turbulence of passive fluids. Here, we perform the first systematic study of active nematic ECS and their invariant manifolds, and discuss their role in characterizing the phenomenon of active turbulence. |
Monday, November 22, 2021 4:57PM - 5:10PM |
P31.00005: nekStab: open-source toolbox for large-scale stability analysis in Nek5000 Jean-Christophe Loiseau, Ricardo Frantz, Jean-Christophe Robinet Over the past decade, stability analyses of complex three-dimensional flows have become feasible. They moreover provide new insights into the early transition mechanisms. Likewise, computing unstable periodic orbits (UPO) is instrumental in understanding turbulence in canonical flows. Few tools are however available in open-source. |
Monday, November 22, 2021 5:10PM - 5:23PM |
P31.00006: The Ladyzhenskaya-Prodi-Serrin Conditions and the Navier-Stokes Blow-Up Problem Bartosz Protas, Di Kang This investigation concerns a systematic search for potentially singular behavior in 3D Navier-Stokes flows. One of the most important conditional regularity results are the Ladyzhenskaya-Prodi-Serrin conditions. They assert that if the quantity $\int_0^T \| \mathbf{u}(t) \|_{L^q(\Omega)}^p \, dt$, where $2/p+3/q \le 1$, $q > 3$, is bounded, then the solution $\mathbf{u}(t)$ of the Navier-Stokes system is smooth on the interval $[0,T]$. In other words, if this quantity is unbounded, a singularity must occur at some time $t \in [0,T]$. We have probed this condition by studying a family of variational optimization problems where initial conditions $\mathbf{u}_0$ are sought to maximize $\int_0^T \| \mathbf{u}(t) \|_{L^q(\Omega)}^p \, dt$ for different $T$ and subject to certain constraints. Such problems are solved computationally using a large-scale adjoint-based gradient approach. Even in this worst-case scenario, no evidence has been found for singularity formation which would be manifested by unbounded growth of $\| \mathbf{u}(t) \|_{L^q(\Omega)}$. However, the maximum enstrophy in these flows scales in proportion to $\mathcal{E}_0^{3/2}$, the same as found by Kang et al.~(2020) when maximizing the finite-time growth of enstrophy. |
Monday, November 22, 2021 5:23PM - 5:36PM |
P31.00007: Bifurcations in the motion of articulated tubes conveying fluid, with an end mass Nikhil Sethukumar, Anil K Bajaj, Mahesh Panchagnula A system of articulated tubes conveying fluid has been studied for its nonlinear behaviour. The dynamics of the two tube system can be studied by varying two parameters: β corresponding to the ratio of masses of the tube and the fluid, and ρ, the dimensionless flow rate. For a particular β, as the flow rate is increased, the zero equilibrium becomes unstable via a Hopf bifurcation, leading to a limit cycle motion centered around the zero equilibrium. When a point mass is attached to the free end of the two tube system, a parameter α corresponding to the ratio of the mass of the point mass to the mass of the tubes and fluid, may be introduced. The obtained numerical solutions to the four first order differential equations suggest that as the end mass is increased, a symmetry-breaking bifurcation results in two stable limit cycle solutions neither centered around the zero equilibrium point. As α is further increased, this is followed by a period-doubling route to chaos. A Poincare section of the four dimensional motion is used to quantify the bifurcation, and is shown to be similar to that of the logistic map with α being the control parameter. |
Monday, November 22, 2021 5:36PM - 5:49PM |
P31.00008: Symmetry-Breaking Bifurcations in Two-Dimensional Square Vortex Flows Balachandra Suri We present a theoretical study of spatial symmetries and bifurcations in a laterally bounded two-dimensional flow composed of approximately square vortices. The numerical setting simulates a laboratory experiment wherein a shallow electrolyte layer is driven by a plane-parallel force that is nearly sinusoidal in both extended directions. Choosing an integer or half-integer number of forcing wavelengths along each direction, we generate square vortex flows invariant under different spatial symmetries. We then map out the sequence of symmetry-breaking bifurcations leading to the formation of fully asymmetric flows. Our analysis reveals a gallery of pitchfork and Hopf bifurcations, both supercritical and subcritical in nature, resulting in either steady or time-dependent asymmetric flows. Furthermore, we demonstrate that different classes of flows (steady, periodic, pre-periodic, or quasi-periodic), at times with two-fold multiplicity, emerge as a result of symmetry-breaking bifurcations. Our results also provide new theoretical insights into previous experimental observations in quasi-two-dimensional square vortex flows. |
Monday, November 22, 2021 5:49PM - 6:02PM |
P31.00009: Computational Study on Fluid Flexible-Solid Interaction-based Chaotic Mixing Characteristics in a Cavity Flow VINAY PRASAD, Atul Sharma, Salil S Kulkarni In our previous work, it was observed that the addition of an elliptic-shaped deformable solid in a simple cavity flow has induced chaotic mixing while the no-solid case showed linear mixing. This work aims to understand the reason behind mixing enhancement due to the presence of a deformable solid. The work focuses on the optimum solid parameters i.e, Aspect Ratio 0.5 and Volume Fraction 10% as obtained from our earlier work, at a constant Capillary number 0.05 and Reynolds number 100. To this end, a detailed investigation was done using non-linear lagrangian dynamical tools, such as Poincare Map Analysis (PMA), Periodic Point Analysis (PPA), and Adaptive Material Tracking (AMT). PMA revealed three clearly visible islands at the core, apart from islands near the stationary walls. PPA revealed the lowest order hyperbolic/elliptic periodic points to be third. AMT gave the physical picture of the deforming material blob revealing its exponential stretch with steep folds. Additionally, unstable /stable manifolds corresponding to lowest order hyperbolic points have been identified. Further study confirmed the existence of heteroclinic connections and tangles in the system. |
Monday, November 22, 2021 6:02PM - 6:15PM |
P31.00010: Wavelength selection of turbulent bands in transitional turbulence Sébastien Gomé, Laurette S Tuckerman, Dwight Barkley Transition to turbulence in shear flows is characterized by oblique turbulent bands. In plane Couette flow, a spacing of λ=40h between the bands naturally arises from featureless turbulence. Below 40h, turbulent bands interact too strongly to coexist naturally, but can be produced in periodic domains of restricted lengths and fixed tilt. The stability of such fixed-wavelength patterns is studied as a function of Reynolds number, as well as the mechanisms giving birth to a wavelength selection from featureless turbulence. |
Monday, November 22, 2021 6:15PM - 6:28PM |
P31.00011: The nonlinear transient growth of supersonic shear flows Zhu Huang, Huangsheng Wei, Guang Xi The linear instability analysis for the flow transition to turbulence in supersonic flow has been studied extensively, including the exponential growth modes know as Mack instability and the linear transient growth. For supersonic flows, the density, velocity and temperature are coupled together to enhance the nonlinear interaction in the flow transition process. However, the fully nonlinear interactions and the related mechanism of the supersonic flows have not been investigated. In this study, we developed a framework to calculate the nonlinear optimal disturbance of supersonic shear flows, including the Couette flow and Poiseuille flow. The fifth order weighted essentially non-oscillatory scheme is employed in the solver of compressible flow in curvilinear coordinates. The nonlinear optimal disturbance is calculated by optimizing the total perturbation energy including the perturbations of density and temperature. The proposed method is validated by the incompressible nonlinear transient growth and the linear transient growth of compressible shear flows. The Mach number effect on the nonlinear optimal disturbance and its nonlinear transient growth is investigated. |
Monday, November 22, 2021 6:28PM - 6:41PM |
P31.00012: The onset of fully turbulent pipe flow Elena Marensi, Björn Hof Transitional turbulence is composed of localized puffs whereas space filling fully turbulent flow only becomes sustained at somewhat larger Reynolds numbers. In the present computational study we introduce a volume forcing that flattens the velocity profile, a method recently used to suppress and even eradicate turbulence in simulations and experiments. Using the forcing amplitude as a control parameter we determine the minimum requirements for fully turbulent flow to be sustained. Interestingly, and despite strongly differing forcing amplitudes, the 'minimal' velocity profiles are found to collapse in inner units and equally collapse with the unforced case at the puff-slug transition point. From these observations we determine the minimum energetic requirements for fully turbulent pipe flow to become sustained and compare these conditions to Couette and channel flow. |
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