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 G8: Nonlinear Dynamics: Turbulence and Transition to Turbulence |
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Chair: Jae Sung Park, University of Wisconsin-Madison Room: B116 |
Monday, November 21, 2016 8:00AM - 8:13AM |
G8.00001: Temporal coherence of turbulent dynamics in minimal channel flow and its connection to exact coherent states Jae Sung Park, Michael Graham The dynamics of the turbulent near-wall region is known to be dominated by coherent structures. These near-wall coherent structures are observed to burst in an intermittent way, exporting turbulent kinetic energy to the rest of the flow. In addition, they are closely related to invariant solutions known as exact coherent states (ECS), some of which display nonlinear critical layer dynamics. In this study, temporal coherence in minimal channel flow relevant to burst and critical layer dynamics is investigated. The turbulence displays frequencies very close to the critical layer frequency displayed by an ECS family recently identified in the channel flow geometry. The bursting frequency is predominant near the wall, while the critical layer frequency becomes predominant over the bursting frequency as we move away from the wall. In particular, the critical layer frequency becomes more prominent near the channel center and at higher Reynolds number. Finally, turbulent bursts are classified into strong and relatively weak classes with respect to an intermittent approach to a lower branch ECS. The relationship between the strong burst class and the instability of the lower branch ECS is further discussed. [Preview Abstract] |
Monday, November 21, 2016 8:13AM - 8:26AM |
G8.00002: Enhanced energy fluxes via phase precession in forced Burgers equation Brendan Murray, Miguel Bustamante, Michele Buzzicotti, Luca Biferale We present a study of phase dynamics in the non-linear forced Burgers' equation. We uncover a connection between energy flux across scales and the evolution of triad phase combinations in Fourier space\footnote{M. Buzzicotti, B. P. Murray, L. Biferale and M. D. Bustamante, \textit{EPJE} \textbf{39(3)}, (2016)}. As this energy is dissipated at small scales, real-space shock structures are associated with entangled correlations amongst the phase precession dynamics and the amplitude evolution of triads in Fourier space. We compute precession frequencies of the triad phases, which show a non-Gaussian distribution with multiple peaks and fat tails, with significant correlation between precession frequencies and amplitude growth. The observed fat tails and non-zero precession frequencies are two key criteria for enhancing energy fluxes via precession resonance\footnote{ M. D. Bustamante, B. Quinn, and D. Lucas, \textit{Phy. Rev. Let.} \textbf{113(8)}, (2014)}. We search for this resonance by varying the forcing strength and frequency and, additionally, by modifying the dimension of the underlying system via fractal Fourier decimation. [Preview Abstract] |
Monday, November 21, 2016 8:26AM - 8:39AM |
G8.00003: A variational method for the identification of nonlinear energy transfers responsible for intermittent fluctuations in turbulent shear flows Mohammad Farazmand, Themis Sapsis It is believed that the intermittent fluctuations in turbulent shear flows are triggered by the energy transfer to the mean flow via nonlinear inertial interactions. However, because of the vast range of active spatial and temporal scales, identifying the responsible interactions is not straightforward. We show that the responsible modes can be formulated as the (initially unknown) solutions of an appropriate constrained variational problem. The variational problem can be solved at a low computational cost, and the solution is the nontrivial mode with instantaneously maximal transfer of energy to the mean flow. We demonstrate the application of this variational method on a direct numerical simulation of a shear flow with external body forcing. [Preview Abstract] |
Monday, November 21, 2016 8:39AM - 8:52AM |
G8.00004: Energy cascade and irreversibility in reversible shell models of turbulence Massimo De Pietro, Massimo Cencini, Luca Biferale, Guido Boffetta Dissipation breaks the time reversibility of the Navier-Stokes equation. It has been conjectured that forced-dissipated Navier-Stokes equations are “equivalent” to a modified version of the equations in which the dissipative term is modified such as to preserve the time-inversion symmetry. This can be realized choosing a velocity dependent viscosity in such a way to preserve a global quantity, e.g. energy or enstrophy. Here we present results on shell models of turbulence where time reversibility is restored following the mechanism originally suggested. We show that when the time-dependent viscosity is chosen such as to conserve enstrophy, the resulting reversible dynamics exhibit an energy cascade, sharing the same features of the standard irreversible cascade. [Preview Abstract] |
Monday, November 21, 2016 8:52AM - 9:05AM |
G8.00005: One-way spatial integration of Navier-Stokes equations: stability of wall-bounded flows Georgios Rigas, Tim Colonius, Aaron Towne, Michael Beyar For three-dimensional flows, questions of stability, receptivity, secondary flows, and coherent structures require the solution of large partial-derivative eigenvalue problems. Reduced-order approximations are thus required for engineering prediction since these problems are often computationally intractable or prohibitively expensive. For spatially slowly evolving flows, such as jets and boundary layers, a regularization of the equations of motion sometimes permits a fast spatial marching procedure that results in a huge reduction in computational cost. Recently, a novel one-way spatial marching algorithm has been developed by Towne & Colonius (JCP 300: 844-861, 2015). The new method overcomes the principle flaw observed in Parabolized Stability Equations (PSE), namely the \emph{ad hoc} regularization that removes upstream propagating modes. The one-way method correctly parabolizes the flow equations based on estimating, in a computationally efficient way, the local spectrum in each cross-stream plane and an efficient spectral filter eliminates modes with upstream group velocity. Results from the application of the method to wall-bounded flows will be presented and compared with predictions from the full linearized compressible Navier-Stokes equations and PSE. [Preview Abstract] |
Monday, November 21, 2016 9:05AM - 9:18AM |
G8.00006: Exact Navier-stokes Solutions in a Compressible 2D Open Cavity Flow Javier Otero, Ati Sharma, Richard Sandberg In very simple geometries and always assuming an incompressible flow, researchers have sought to understand the flow physics by looking for steady or periodic flow solutions. These solutions exactly satisfy the governing equations, and determine the physics of the flow. In the current investigation we perform for the first time this type of analysis in a compressible flow and in a complex geometry. In particular, we focus on a 2D laminar inflow open cavity flow at $Re=2000$, which is simulated using an in-house compressible DNS code. Initially, an exact periodic flow solution is found at $M=0.5$, which shows a novel noise generation mechanism that we explain in detail. This periodic flow solution is continued across Mach number, covering from M = 0.25 to M = 0.8. At the lower end of the range, the periodic solution ceases to exist due to the low compressibility of the system and leads to a steady state. This steady solution can be seen as the bifurcation point between the family of steady and periodic solutions. [Preview Abstract] |
Monday, November 21, 2016 9:18AM - 9:31AM |
G8.00007: Near critical swirling flow of a viscoelastic fluid Nguyen Ly, Zvi Rusak, John Tichy, Shixiao Wang The interaction between flow inertia and elasticity in high Re, axisymmetric, and near-critical swirling flows of a viscoelastic fluid in a finite-length straight circular pipe is studied. The viscous stresses are described by the Giesekus constitutive model. The application of this model to columnar streamwise vortices is first investigated. Then, a nonlinear small-disturbance analysis is developed from the governing equations of motion. It explores the complicated interactions between flow inertia, swirl, and fluid viscosity and elasticity. An effective Re that links between steady states of swirling flows of a viscoelastic fluid and those of a Newtonian fluid is revealed. The effects of the fluid viscosity, relaxation time, retardation time and mobility parameter on the flow development and on the critical swirl for the appearance of vortex breakdown are explored. Decreasing the ratio of the viscoelastic characteristic times from one increases the critical swirl for breakdown. Increasing the Weissenberg number from zero or increasing the fluid mobility parameter from zero cause a similar effect. Results may explain changes in the appearance of breakdown zones as a function of swirl level that were observed in Stokes {\it et al.} (2001) experiments, where Boger fluids were used. [Preview Abstract] |
Monday, November 21, 2016 9:31AM - 9:44AM |
G8.00008: Subcritical Transition to Turbulence in Couette-Poiseuille flow Jose Eduardo Wesfreid, Lukasz Klotz We study the subcritical transition to turbulence in the plane Couette-Poiseuille shear flow with zero mean advection velocity. Our experimental configuration consists on one moving wall of the test section (the second one remains stationary), which acts like a driving force for the flow, imposing linear streamwise velocity profile (Couette) and adverse pressure gradient in the streamwise direction (Poiseuille) at the same time. This flow, which had only been studied theoretically up to now, is always linearly stable. The transition to turbulence is forced by a very well controlled finite-size perturbation by injection, into the test section, of a water jet during a very short time. Using PIV technique, we characterized quantitatively the initial development of the triggered turbulent spot and compared its energy evolution with the theoretical predictions of the transient growth theory. In addition, we show results concerning the importance of nonlinearities, when waviness of streaks in streamwise direction induced self-sustained process in the turbulent spot. We also measured precisely the large-scale flow which is generated around the turbulent spot and studied its strength as a function of the Reynolds number. [Preview Abstract] |
Monday, November 21, 2016 9:44AM - 9:57AM |
G8.00009: Experimental and numerical study of direct laminar-turbulent transition in Taylor-Couette flow Christopher J. Crowley, Michael Krygier, Daniel Borrero-Echeverry, Roman O. Grigoriev, Michael F. Schatz The transition to turbulence in large aspect ratio Taylor-Couette flow (TCF) occurs via a sequence of supercritical bifurcations of stable flow states (e.g. spiral vortices, interpenetrating spirals (IPS), and wavy interpenetrating spirals). We previously reported the discovery of a direct laminar-turbulent transition in a TCF system with counter-rotating cylinders (Re$_o = -1000$, Re$_i \approx 640$) and a small aspect ratio ($\Gamma = 5.26$) as Re$_i$ is slowly increased. This transition is mediated by an unstable IPS state. As Re$_i$ is decreased, the turbulent flow first relaminarizes into an intermediate, stable IPS state, before returning to circular Couette flow. In this talk we will present the study of this transition experimentally using tomographic PIV and direct numerical simulations with realistic boundary conditions, and show that it is both highly repeatable and that it shows hysteresis. The transition between both the IPS and turbulent states exhibits statistics consistent with chaotic attractor transitioning to a chaotic repeller. The IPS state is accessed from a subcritical transition and is inaccessible when the inner cylinder is originally accelerated on the way up to turbulence, suggesting that a finite amplitude perturbation is required to reach it. [Preview Abstract] |
Monday, November 21, 2016 9:57AM - 10:10AM |
G8.00010: Connections between large-domain Newtonian turbulence and minimal-channel exact coherent states Anubhav Kushwaha, Michael Graham Direct numerical simulations (DNS) of plane Poiseuille flow of a Newtonian fluid are performed in a large domain at transitional Reynolds numbers. In this Reynolds number regime, turbulent trajectories in minimal channels move chaotically between lower and upper branch invariant solutions known as exact coherent states (ECS). It is found that while they spend most of the time in a core region of the state space, fluctuating about the upper branch ECS, they occasionally escape the core region and pass through the vicinity of lower branch solutions. One particular set of the lower branch solutions form the lower bound of the turbulent trajectory with regard to flow properties like wall shear stress, energy dissipation rate and turbulent kinetic energy. We compare the evolution of wall shear stress in minimal channels with those in patches the size of minimal channels in a large domain and find that they are not only indistinguishable but also bounded on the lower end by the same set of lower branch ECS. This suggests that localised regions in a large box approach the travelling wave solutions in a way similar to minimal channels. We also show that low and high drag regions occur spatiotemporally when the turbulence trajectory approaches the lower and upper branch ECS, respectively. [Preview Abstract] |
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