Bulletin of the American Physical Society
75th Annual Meeting of the Division of Fluid Dynamics
Volume 67, Number 19
Sunday–Tuesday, November 20–22, 2022; Indiana Convention Center, Indianapolis, Indiana.
Session U18: Turbulence: Theory II |
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Chair: Adrian van Kan, UC Berkeley; Joachim Peinke, University of Oldenburg Room: 145 |
Tuesday, November 22, 2022 8:00AM - 8:13AM |
U18.00001: Spontaneous suppression of the inverse energy cascade and formation of vortex crystals in instability-driven two-dimensional turbulence Adrian van Kan, Benjamin Favier, Keith A Julien, Edgar Knobloch Instabilities of fluid flows often generate turbulence. Using extensive direct numerical simulations, we study two-dimensional turbulence driven by a wavenumber-localised instability superposed on stochastic forcing, in contrast to previous studies of state-independent forcing. As the instability growth rate $\gamma$ increases, the system undergoes two transitions. For growth rates below a first threshold $\gamma<\gamma_1$, a regular large-scale vortex condensate (LSC) forms. For $\gamma \geq \gamma_1$, shielded vortices (SVs) emerge and coexist with the condensate. At a second, larger value $\gamma_2$ of the growth rate, the condensate breaks down, and a gas of weakly interacting vortices with broken symmetry spontaneously emerges, characterised by preponderance of vortices of one sign only and suppressed inverse energy cascade. The number density of SVs in this broken symmetry state slowly increases via a random nucleation process. In the late-time limit a dense SV gas emerges, which persists down to small growth rates, where it crystallises to form a hexagonal lattice. Bi- and multistability is observed between the LSC, the mixed LSC-SV and the dense SV states over a wide range of growth rates. Our findings provide new evidence for a strong dependence of two-dimensional turbulence phenomenology on the forcing. |
Tuesday, November 22, 2022 8:13AM - 8:26AM |
U18.00002: Understanding non-universal scaling for the direct cascade in 2D flows Mateo A Reynoso, Roman O Grigoriev For high-Re turbulent 2D flows, the Kraichnan-Leith-Batchelor theory predicts that the energy density scales as an integral power of the wavenumber, E(k) ~ k-3, in the inertial range. However, experiments and numerical simulations generally find spectra exhibiting scaling with fractal exponents. In this work, we consider statistically stationary 2D turbulent flows on a domain with periodic boundary conditions where forcing is balanced by viscous dissipation. We explore how the folding and stretching of vorticity filaments by the large-scale flow (LSF) generates self-similar structures characterized by fractal spectra. We show that the fractal exponent depends on the properties of the LSF which, in turn, depend on the forcing and boundary conditions. |
Tuesday, November 22, 2022 8:26AM - 8:39AM |
U18.00003: Instantons and the path to intermittency in turbulent flows André Fuchs, Corentin Herbert, Joran Rolland, Matthias Wächter, Freddy Bouchet, Joachim Peinke Processes leading to anomalous fluctuations in turbulent flows, referred to as intermittency, are still challenging. We consider cascade trajectories through scales as realizations of a stochastic Langevin process for which multiplicative noise is an intrinsic feature of the turbulent state. The trajectories are conditioned on their entropy exchange. Such selected trajectories concentrate around an optimal path, called instanton, which is the minimum of an effective action. The action is derived from the Langevin equation, estimated from measured data. In particular, instantons with negative entropy pinpoint the trajectories responsible for the emergence of non-Gaussian statistics at small-scales. |
Tuesday, November 22, 2022 8:39AM - 8:52AM |
U18.00004: Worm's characteristics in 'classical' and 'non-equilibrium' turbulence Afonso Ghira, Gerrit E Elsinga, Carlos B da Silva The characteristics of the intense vorticity structures or 'worms' are analysed in direct numerical simulations (DNS) of isotropic turbulence in i) 'classical' and ii) 'non-equilibrium' turbulence, where the two types of turbulence/simulations are achieved by manipulating the forcing applied at the large scale motions. |
Tuesday, November 22, 2022 8:52AM - 9:05AM |
U18.00005: On turbulent/non-turbulent interfaces from equilibrium and non-equilibrium turbulence Marco Zecchetto, Carlos B da Silva Direct numerical simulations (DNS) of turbulent fronts created by both equilibrium and non-equilibrium (unbalanced) turbulence are used to assess the characteristics of the turbulent/non-turbulent interface (TNTI) that separates regions of turbulent from non-turbulent (or irrotational) flow. The effects of the unbalance can be observed in the detailed shape of the conditional profiles of vorticity magnitude, and in the magnitude of the maximum enstrophy but do not affect its main features. |
Tuesday, November 22, 2022 9:05AM - 9:18AM |
U18.00006: Mechanisms toward Kolmogorov's isotropy Chang Hsin Chen, Diego A Donzis Universality is a fundamental concept in turbulence which rests on the assumption of statistically isotropic motions at Kolmogorov scales. However, such mechanical equilibrium can be disrupted by different mechanisms such as shocks and shear. A pervasive and long-standing related question is on the specific dynamical processes involved in driving the system towards local isotropy. To study these turbulent processes, we present a theoretical analysis that unveils the mechanisms that drive the flows back to equilibrium at the small scales. Surprisingly, the mechanisms are found to be of dissipative nature. To study these findings, we use a database of direct numerical simulations of shock-turbulence interactions, a canonical well-studied flow configuration which provides a strong enough shear to induce non-equilibrium at Kolmogorov scales and study in detail the proposed mechanism. The database includes both the so-called wrinkled and broken regimes of the interactions which involve varying degrees of relative turbulence intensities. The DNS data show that the dissipative mechanisms peak at post-shock regions and decay monotonically as turbulence achieves equilibrium. In addition, the mechanisms are found to be more dominant in the wrinkled regime resulting in a stronger reduction of anisotropy. Despite their dissipative nature, the observations show that the mechanisms can be positive locally. |
Tuesday, November 22, 2022 9:18AM - 9:31AM |
U18.00007: Why is the Reynolds Stress Realizable, but Not Objective? Charles A Petty The Coriollis Theorem of classical kinematics predicts that the strain rate is temporally frame insensitive for all turbulent flows; and, that the Reynolds stress is temporally frame sensitive for all turbulent flows. Consequently, the Cauchy stress and the Reynolds stress are not similar. Most significantly, the Reynolds stress predicts that the turbulent dispersion and the turbulent dissipation of turbulent kinetic energy are both positive; and, the production of kinetic energy could be either positive or negative. See Koppula K.S., A. Benard, and C. A. Petty, 2009, Realizable Algebraic Reynolds Stress Closure, Chem. Eng. Sci., 64, 4611. |
Tuesday, November 22, 2022 9:31AM - 9:44AM |
U18.00008: Influence of thermal non-equilibrium on the dynamics of velocity gradient in turbulent flows SHISHIR SRIVASTAVA, Sawan S Sinha Dynamics of velocity gradient is a useful tool for understanding several non-linear turbulent processes of interest and has been widely employed to investigate various fundamental aspects of incompressible turbulent flows. However, such research on compressible turbulence and that, especially, under thermal non-equilibrium (TNE) conditions is minimal. Flow fields associated with TNE are characterized by complexities including but not limited to (i) a significant level of divergence in the velocity field, (ii) thermodynamic nature of pressure evolution (iii) vibrational excitation and subsequent dissociation of the constituent air molecules. These challenges are often encountered in hypersonic flows that exist past objects/vehicles re-entering the earth's (or other planetary) atmosphere. The primary focus of the present work is to first develop the exact theoretical formulation of the evolution equations of the velocity gradient and the pressure-hessian tensor. Subsequently, we identify the dominant unclosed processes in this formulation. Finally, we make attempts to model these dominant processes to capture the essential influence of TNE on compressible velocity gradient dynamics. |
Tuesday, November 22, 2022 9:44AM - 9:57AM |
U18.00009: How accurate is Morkovin's hypothesis for supersonic wall-bounded turbulent flows? Asif Manzoor Hasan, Johan Larsson, Sergio Pirozzoli, Rene Pecnik Despite extensive research and significant progress in the past decades on wall-bounded turbulence with strong heat transfer and high flow speeds, the underlying turbulence modifications are yet not fully understood. In the non-hypersonic regime, these modifications are generally understood to be a consequence of mean property variations (Morkovin's hypothesis). We perform DNS of supersonic channel flows, cancelling the effect of aerodynamic heating, to obtain negligible mean property variations. Contrary to the expectation that these cases will have negligible effects of compressibility, we observed non-negligible effects especially near the wall. Using Helmholtz decomposition, we observed that the inter-component energy transfer among the solenoidal Reynolds stresses reduces with increasing Mach number. This clearly indicates an indirect compressibility effect on the solenoidal component of velocity. |
Tuesday, November 22, 2022 9:57AM - 10:10AM |
U18.00010: Causally significant structures in isotropic turbulence at low Reynolds number Xinxian Zhang, Javier Jimenez, Chong Pan A large number of numerical experiments with 3D direct numerical simulations of homogeneous isotropic turbulence (HIT) are conducted at Reynolds number Reλ≈50, to investigate the causally significant turbulent structures in HIT at low Reynolds number. We first determine whether significant flow regions exist, and then examine whether they share some common characteristics. To do this, 65 basic initial flows are created, and each of them is divided into 103 cubical cells. The flow in each cell is modified, the effect of the modification on the flow is monitored, and casually significant cells are defined as those in which the modification leads to a large overall change in the flow at a later measurement time. In our study, the flow within each cell is modified in eight ways, including in both vorticity and velocity fields. The process is repeated for each cell and each kind of modification, for a total of 5.2×105 simulations. Our results indicate that significant regions exist in HIT at low Reynolds number. The most sensitive cells in experiments involving vorticity are those with initial high enstrophy, while velocity experiments select regions with high initial kinetic energy. The structure and other characteristics of these significant regions are studied. |
Tuesday, November 22, 2022 10:10AM - 10:23AM |
U18.00011: Characterizing the energy cascade using the zero-crossings of the longitudinal velocity fluctuations Martin Obligado, Amelie Ferran, Alberto Aliseda It is well known that the zero-crossings of the longitudinal velocity fluctuations allow to estimate the Taylor length scale of turbulence thanks to the Rice theorem. Furthermore, it has recently been found (Mora \& Obligado, Exp. Fluids, 2020) that they can also be used to compute its integral length scale. In consequence, they can be exploited to study several one-point statistics from a turbulent flow. Such approach presents several advantages as it enables to characterize a turbulent flow in extremely challenging situations, where the flow is unsteady or a proper calibration of the equipment cannot be guaranteed. |
Tuesday, November 22, 2022 10:23AM - 10:36AM |
U18.00012: Symmetry analysis of the turbulent dissipation rate Kalale Chola, Pinaki Chakraborty A core attribute of any turbulent flow is the rate at which it dissipates energy ε. In his classic study from 1935, Taylor invoked rotational symmetry to transform the original cumbersome expression for ε into a remarkably simple formula but for which it would be practically impossible to compute ε in most experiments. Taylor's analysis, though ingenious, leaves it unclear if the formula truly conforms with rotational symmetry. We use the rigorous approach of Lie groups and show that Taylor's formula indeed holds for rotational symmetry. Further, we find that the formula is surprisingly robust—it holds, as is, for a distinctly different symmetry: reflectional symmetry. Additionally, we highlight that the widely used tests for identifying flow symmetries can yield misleading results. With rigor, precision, and clarity, the machinery of Lie groups delineates the underlying symmetries that dictate turbulent flows. |
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