Bulletin of the American Physical Society
76th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 19–21, 2023; Washington, DC
Session L42: Turbulence: Theory I |
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Chair: Sharath Girimaji, Texas A&M University Room: 207A |
Monday, November 20, 2023 8:00AM - 8:13AM |
L42.00001: Inertial transfer and small-scale structures in magnetohydrodynamic turbulence Damiano Capocci, Sean Oughton, Perry L Johnson, Luca Biferale, Moritz Linkmann In homogeneous magnetohydrodynamic (MHD) turbulence, simulation results indicate a depletion of the interscale kinetic energy flux associated with the inertial term relative to the hydrodynamic (HD) case. Here we report on an investigation of the physical mechanisms behind this depletion, analysing the role of the contractile and extensional directions of the velocity gradient tensor. Because of incompressibility, there are only two possible types of deformation than a small sphere of fluid can undergo when subject to strain. It may either flatten and become disk-shaped, due to one contractile and two extensional directions of the strain tensor, or it may elongate in one direction and become cigar-shaped, due to two contractile and one extensional directions. Using simulation data we find that for MHD turbulence the two types of deformation are approximately equally probable, while in HD turbulence disk-like flattening is known to be the dominant feature, associated with strain self-amplification and vortex stretching. This suggests that the small-scale structure of MHD turbulence is fundamentally different from HD turbulence. We will discuss a theoretical ansatz to explain the impact of the Lorentz force on the compressive and contractile flow directions. |
Monday, November 20, 2023 8:13AM - 8:26AM |
L42.00002: Utilizing intra-triad energy conservation for phase reconstruction from low-order statistics Miya Y Coimbra, Benedikt Barthel, Greg P Chini, Beverley J McKeon We present a formulation for analytically determining phase information from the magnitude of the Fourier modes, or the mode shapes and amplitudes, in turbulent channel flow. This is done by utilizing the fact that nonlinear terms in the Navier-Stokes equations are energy conserving within a set of triadically consistent wavenumbers, an observation originally made by Schmid and Henningson (2001) and explored by Barthel (2022). The proposed algorithm successfully predicts the trends in phase shift between a set of triads, relative to an unknown reference mode, showing agreement within 15% when compared to DNS results. This work has broader implications in the context of utilizing the scalability of low-order moments, such as the power spectrum, while still retaining relative phase information, which is generally only present in higher order statistics. Two-point and space-time correlations provide some phase information; however, their computation requires knowledge of the full velocity field. The power spectrum lacks any directional information but holds the advantage that it can be computed via scaling from a lower Reynolds number spectrum. The reconstruction of relative phase shifts from the power spectrum has the potential to reintroduce directional information to low-order statistics, allowing for more complete and computationally accessible representations of high Reynolds number turbulent flows. |
Monday, November 20, 2023 8:26AM - 8:39AM |
L42.00003: Higher-order statistics and intermittency of a two-fluid HVBK quantum turbulent flow Luminita Danaila, Zhentong Zhang, Emmanuel Lévêque, Ionut Danaila The Hall-Vinen-Bekharevich-Khalatnikov (HVBK) model is widely used to study quantum turbulence in superfluid helium numerically. Based on the two-fluid model of Tisza and Landau, the HVBK model describes the normal (viscous) and superfluid (inviscid) components of the flow using two Navier-Stokes type equations coupled through a mutual friction force term. |
Monday, November 20, 2023 8:39AM - 8:52AM |
L42.00004: Action of pressure fluctuations in turbulent flows – the principle of least effort Rishita Das, Sharath S Girimaji In incompressible fluid flow, pressure is a Lagrange multiplier whose sole function is to impose the divergence-free condition on the velocity field. While the role of pressure is well recognized, the manner in which pressure enforces the constraint is not well known. Understanding this action of pressure is important as it plays a critical role in determining characteristics of the turbulence small scales. Following our previous work (Das & Girimaji APS DFD 2018), we examine the hypothesis that pressure accomplishes its task with minimum action or least effort. In recent literature, it has been proven analytically that in elementary flows, pressure gradient is minimized following Gauss' principle of least constraint. For turbulent flows, such analytical treatment is not possible due to flow complexity, non-locality, and nonlinearity. We propose two metrics of pressure effort based on the principle of least constraint. Then, we use direct numerical simulation (DNS) data to demonstrate that pressure action in velocity-gradient dynamics is consistent with the simultaneous minimization of the two proposed metrics. The findings can lead to improved models for anisotropic pressure Hessian tensor. |
Monday, November 20, 2023 8:52AM - 9:05AM |
L42.00005: Pattern formation by turbulent cascades: the case of odd viscosity Xander M de Wit, Michel Fruchart, Tali Khain, Federico Toschi, Vincenzo Vitelli We study the influence of non-dissipative viscosity on fluid turbulence. Such viscosity, called odd, Hall or gyro viscosity, can emerge in chiral systems ranging from plasma and bio-active media to quantum fluids. We show that odd viscosity has a tendency to revert the turbulent cascade at a characteristic length scale, leading to a non-dissipative arrest of the kinetic energy transfer and hence accumulation of energy at intermediate scales. We identify this as a paradigmatic example of non-linear pattern formation. The observed phenomenology can be understood from a generalization of the Taylor-Proudman theorem, leading to an interpretation of odd viscosity as an effective, wavenumber dependent rotation, which crucially has a stronger effect at larger wavenumbers, contrary to canonical rotating turbulence. The fundamental consequence, which we unveil using a combination of large scale simulations and scaling theory, is that both direct and inverse energy cascades carry energy to the characteristic intermediate scale, leading to selection of a dominant wavelength in the flow. Beyond odd viscosity, this type of cascade-induced pattern formation may play an important role in several natural systems including atmospheric flows, stellar plasma such as the solar wind, as well as the pulverization of objects or the coagulation of droplets where mass rather than energy cascades. |
Monday, November 20, 2023 9:05AM - 9:18AM |
L42.00006: Two-way coupled simulation of quantum turbulence and normal-fluid turbulence in superfluid helium-4 Hiromichi Kobayashi, Satoshi Yui, Makoto Tsubota, Tomokazu Saito, Rio Yokota We numerically demonstrate the two-way coupled simulation of quantum turbulence and normal-fluid turbulence in superfluid helium-4. In less than 2.17 K, the superfluid helium is composed of an inviscid superfluid component and a viscous normal-fluid component. The velocity circulation of the superfluid component is quantized, and the superfluid component exists as quantized vortex lines. The tangled vortex line is called quantum turbulence. In the externally driven normal-fluid turbulence, the quantized vortex lines are stretched via mutual friction with normal-fluid and reconnect with each other. Eventually, the transition to quantum turbulence occurs. The quantized vortex lines are bundled in the normal-fluid vortex tubes. This is one of the reasons why the superfluid exhibits the K41 energy spectrum. |
Monday, November 20, 2023 9:18AM - 9:31AM |
L42.00007: Turbulence Intermittency - Contributing Mechanisms Sharath S Girimaji, Rishita Das Velocity-gradient (VG) intermittency is one of the most intriguing aspects of high Reynolds number turbulence. The Reynolds number scaling of various high-order VG moments have been extensively investigated in literature. However, the physical mechanisms that lead to intermittency have not been as widely studied. As energy cascades to smaller scales, the viscous dissipation must keep pace resulting is increasingly steeper velocity gradients. On an average, cascade rate balances viscous dissipation. At high Reynolds numbers, dissipation is not uniformly distributed in space, but is highly sporadic. In this work, we use direct numerical simulation data to examine if intermittency is merely due to the local imbalance between cascade and viscous dissipation, or caused by other phenomena. We focus specifically on non-local effects. We also demonstrate that the internal geometry of the VG tensor is nearly independent Reynolds number. Further, velocity gradient triple decomposition is used to exhibit that the largest values of dissipation occur in regions of pure shear, rather than solid body rotation. Thus, the enstrophy intermittency is due to shear, rather than solid-body rotation. |
Monday, November 20, 2023 9:31AM - 9:44AM |
L42.00008: Effects of arithmetic precision in large-scale direct numerical simulation of incompressible turbulence in a periodic box Takashi Ishihara, Naoya Okamoto, Mitsuo Yokokawa, Yukio Kaneda The recent development of parallel computers enables us to perform large-scale direct numerical simulations (DNS) of turbulence and to analyze physical quantities with a wider range of scale ratios. One issue to be cared about in such simulations is the effects of arithmetic precision. In this study, to investigate the effects on large-scale DNS, we performed DNSs of incompressible turbulence in a periodic box with single- and double-precision at R_{λ}=170 and R_{λ}=268 based on a spectral method at spatial resolution k_{max}η∼4 and compared the results, where R_{λ} is the Reynolds number based on the Taylor microscale, k_{max} is the maximum retained wavenumber, and η is the Kolmogorov length scale. Particular attention is paid to the time evolution of the spatial maximum of local enstrophy and that of the local energy-dissipation rate. The DNSs show that for R_{λ}=268, unlike the case for R_{λ}=170, the difference between the time evolution by double-precision and that of single-precision is not significant for a short-time range (t < 1.3T) but becomes significant for a long-time range (t > 1.3T). Here, T is a large-scale characteristic timescale. The presentation will also report results regarding some other quantities (including the temporally averaged PDFs). |
Monday, November 20, 2023 9:44AM - 9:57AM |
L42.00009: Effects of anisotropy on the geometry of tracer particle trajectories in turbulent flows Yasmin Hengster, Martin Lellep, Julian Weigel, Matthew Bross, Johannes Bosbach, Daniel Schanz, Andreas Schröder, Florian Huhn, Matteo Novara, Daniel Garaboa Paz, Christian J Kähler, Moritz Linkmann Using curvature and torsion to describe Lagrangian trajectories gives a full description of these as well as an insight into small and large time scales. Here, we compare curvature and torsion probability density functions (PDFs) for Lagrangian trajectories obtained from experimental data using the Shake-the-Box algorithm for turbulent von Kármán flow, Rayleigh Bénard convection and a zero-pressure-gradient (ZPG) boundary layer over a flat plate. The results for the von Kármán flow and Rayleigh-Bénard convection compare and well with those obtained previously from numerical data for homogeneous and isotropic turbulence. Results for the logarithmic layer within the boundary layer differ. To detect and quantify the effect of anisotropy either resulting from a mean flow or large-scale coherent motions on the geometry of tracer particle trajectories, we introduce the curvature vector. We connect its statistics with those of velocity fluctuations and demonstrate that strong large-scale motion in a given spatial direction results in meandering rather than helical trajectories. |
Monday, November 20, 2023 9:57AM - 10:10AM |
L42.00010: Nonuniversality and Dissipative Anomaly in Compressible Magnetohydrodynamic Turbulence Cheng Li, Yan Yang, William H Matthaeus, Bin Jiang, Minping Wan, Shiyi Chen We systematically study the dissipative anomaly in compressible magnetohydrodynamic (MHD) turbulence using direct numerical simulations, and show that the total dissipation remains finite as viscosity diminishes. The dimensionless dissipation rate C_{ε }fits well with the model C_{ε }= _{ }C_{ε,∞ }+ D/R_{L} for all the level of flow compressibility considered here, where R_{L }is the generalized large-scale Reynolds number. The asymptotic value C_{ε,∞} describes the total energy transfer flux, and decreases with increase of the flow compressibility, indicating nonuniversality of the dimensionless dissipation rate in compressible MHD turbulence. After introducing an empirically modified dissipation rate, the data from compressible cases collapse to a form similar to the incompressible MHD case depending only on modified Reynolds number. |
Monday, November 20, 2023 10:10AM - 10:23AM |
L42.00011: Beyond self-similarity in homogenous turbulence Konstantinos Steiros The idea that homogenous turbulence follows a self-similar evolution when it is freely decaying is not new in the turbulence literature (see for instance George PoF 1992). However, self-similarity is generally accepted to be valid (if at all) far from initial conditions, i.e. several turnover times after the onset of decay. At earlier times, self-similarity is less likely to be valid, as the flow evolution strongly depends on its initial conditions and flow history, rather than exclusively on "local" flow physics. Currently, no concrete theoretical framework exists for the description of this early non self-similar evolution, which exhibits important phenomena, as for instance a universal non-classical dissipation scaling (see Vassilicos ARFM 2015). In this talk, I will present a theoretical and numerical (DNS) analysis of this early-stage evolution of turbulence. I will derive non self-similar expressions for the various quantities of interest, and a non power-law decay equation for the turbulence kinetic energy. Contrary to the classical self-similar analysis, the various quantities are depedent on terms which express the influence of the initial conditions, and the departure of the flow from them. |
Monday, November 20, 2023 10:23AM - 10:36AM |
L42.00012: Noise-Induced Transitions in Anisotropic Two-Dimensional Turbulence Lichuan Xu, Adrian van Kan, Chang Liu, Edgar Knobloch Two-dimensional (2D) turbulence features an inverse energy cascade that produces large-scale flow structures such as hurricane-like large-scale vortices (LSVs) and jets. We investigate the dynamics of such large-scale structures using extensive direct numerical simulations of stochastically forced 2D turbulence in a periodic rectangular domain. LSVs form in the system when the aspect ratio δ≈1 and unidirectional jets arise at δ≳1.1. At intermediate δ, noise-induced transitions occur between LSVs and jets. We collect detailed statistics on the lifetimes of these structures, revealing an approximately exponential dependence of the mean lifetime on δ. We also analyze how the lifetimes are impacted by varying the Reynolds number and the scale separation between forcing scale and domain size. The system is found to traverse the same path in Fourier space when transitioning from LSVs to jets and vice versa. In highly elongated domains (δ≫1), an array of jets forms, where the number of jets tends to increase with δ, albeit irregularly. Noise-induced transitions also occur between different numbers of jets. The profiles of the jets in this system are sinusoidal, in contrast with jets on the beta plane. Our findings shed new light on the dynamics of LSVs and jets in anisotropic turbulence. |
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