Bulletin of the American Physical Society
72nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 64, Number 13
Saturday–Tuesday, November 23–26, 2019; Seattle, Washington
Session B28: Turbulence Theory: Spectral Transfer |
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Chair: Stavros Tavoularis, University of Ottawa Room: 610 |
Saturday, November 23, 2019 4:40PM - 4:53PM |
B28.00001: Fluctuations in spectral energy transfer and their consequences Sualeh Khurshid, Diego Donzis, Katepalli Sreenivasan The assumption in Kolmogorov's seminal work, as well as in all the subsequent work of that genre, is that the average energy transfer across scales is unidirectional, from the large to the smallâ€”or, in the case of homogeneous turbulence, from low wavenumbers to high wavenumbers. This assumption would be quite acceptable if the fluctuations in the energy transfer rate were small compared to the mean. But the energy transfer rate is a highly fluctuating quantity, which is nearly as often in the backward direction as forward, and the mean transfer is only a small difference between the two, suggesting the need to consider fluctuations explicitly. In this work, we characterize the fluctuations in wavenumber space, of the energy itself and energy transfer rate, for a range of Reynolds numbers, using highly resolved direct numerical simulations. The simulations allow us to study dynamical interactions across scales and quantitatively address questions such as localness or otherwise of energy transfer in the spectral space. We show that the total transfer rate is indeed local in wavenumber space, though the information about large scales is preserved by means of the low-frequency and low-amplitude fluctuations that traverse from low to high wavenumbers with increasing time lag. [Preview Abstract] |
Saturday, November 23, 2019 4:53PM - 5:06PM |
B28.00002: Emergence of turbulent behavior for passive scalars Diego Donzis, K.R. Sreenivasan, V. Yakhot We recently identified a transition to strong turbulence in isotropic turbulence with stochastic forcing. We found that the higher the order of the derivative moment the lower the transition Reynolds number. By a suitably rescaling, we could reduce the transition value to a universal Reynolds number of the order 10 for all orders. The moments of velocity gradients are Gaussian below this transition Reynolds number and exhibit anomalous scaling above, with the same scaling exponents as high-Reynolds-number turbulence. The matching of the two asymptotic states led to analytical expressions for scaling exponents in excellent agreement with available data. In this work we extend these concepts to passive scalar mixing. We observe a similar type of transition with the same Gaussian asymptotic behavior at low Reynolds numbers, but the transition Reynolds number depends on the Schmidt number (the ratio of viscosity to scalar diffusivity), and the matching of the two regimes yields scaling exponents that depend on the Schmidt number. The connection with the so-called ramp-cliff structures is also discussed. As for the velocity field, these results suggests that high-Reynolds-number behavior can be studied via well-resolved simulations around this low-Reynolds-number transition. [Preview Abstract] |
Saturday, November 23, 2019 5:06PM - 5:19PM |
B28.00003: Third-order structure functions for isotropic turbulence with bidirectional energy transfer Jin-Han Xie, Oliver Buhler We derive and test a new heuristic theory for third-order structure functions that resolve the forcing scale in the scenario of simultaneous spectral energy transfer to both small and large scales, which can occur naturally in rotating stratified turbulence or magnetohydrodynamical turbulence, for example. The theory has three parameters, namely the upscale/downscale energy transfer rates and the forcing scale, and it includes the classic inertial range theories as local limits. When applied to measured data, our global-in-scale theory can deduce the energy transfer rates using the full range of data, therefore it has broader applications compared with the local theories, especially in the situations where the data is imperfect. In addition, because of the resolution of forcing scales, the new theory can detect the scales of energy input, which was impossible before. We test our new theory with a two-dimensional simulation of MHD turbulence and use the theory to analysis geophysical fluid data. [Preview Abstract] |
Saturday, November 23, 2019 5:19PM - 5:32PM |
B28.00004: Inter-scale energy transfer by multiscale vorticity stretching and strain self-amplification in turbulence Perry Johnson Three-dimensional turbulent flows are characterized by net transfer of energy from large to small scales. This inter-scale energy transfer is commonly described as a cascade driven by vorticity stretching, but in a phenomenological or imprecise way. Somewhat less commonly, the role of strain self-amplification is emphasized. This talk demonstrates an exact expression for inter-scale energy transfer in terms of multiscale vorticity stretching and strain self-amplification. This relationship elucidates the relative role of these two mechanisms in driving the cascade in the inertial range, while also accounting for the relative importance of scale-local and scale-nonlocal processes. Direct numerical simulations show that strain self-amplification contributes more to the energy cascade than vorticity stretching, but not overwhelmingly so. The leaky cascade view of inter-scale energy transfer is supported by the results. An additional mechanism of inter-scale energy transfer is revealed, with a possible connection to two-dimensional turbulence. [Preview Abstract] |
Saturday, November 23, 2019 5:32PM - 5:45PM |
B28.00005: Interscale Transport of the Reynolds Shear Stress in Wall-bounded Flows Ramis \"Orl\"u, Giole Ferrante, Andres Morfin, Takuya Kawata, Philipp Schlatter, P. Henrik Alfredsson The interplay between the inner and outer layers in wall-bounded turbulent flows has become one of the focus areas with the advent of high-fidelity numerical and experimental data of sufficient scale separation, i.e.\ high enough Reynolds number. The general view is that the inner layer behaves autonomously in terms of its near-wall cycle and the outer layer exhibits independence of the details of the inner layer. At the same time, strict inner scaling for the near-wall region does not hold, due to the top-down influence from the large-scale structures further away from the wall. Recently, bottom-up influence (inverse energy transfer) has been observed, but primarily studied in terms of the turbulent kinetic energy. Here, using numerical simulation data from both a plane Couette flow and a turbulent boundary layer, the interscale transport of the Reynolds stress is examined. Besides the classical interscale transport of turbulent kinetic energy towards smaller scales, also an inverse interscale transport of the Reynolds shear stress was observed. The spectral, scale-by-scale, analysis also indicates how interscale transport and turbulent diffusion explains the mismatch between the locations of the outer peaks in the Reynolds shear stress production and cospectrum. [Preview Abstract] |
Saturday, November 23, 2019 5:45PM - 5:58PM |
B28.00006: Impact of large-scale flow states on small-scale 3D turbulence Cristian C Lalescu, Michael Wilczek Turbulent flows often feature an intricate interplay between anisotropic, even quasi-two-dimensional, large-scale features and three-dimensional small-scale fluctuations. To systematically study the relation between large-scale flow structures and small-scale turbulence, we investigate a conceptually simple shear flow -- a generalized turbulent Kolmogorov flow. The flow is forced with a single shear mode and is subject to large-scale friction, which effectively allows to control transitions between different large-scale states. We present a detailed investigation of the energetics of the system, and we find that the excitation of three-dimensional small-scale turbulence provides a dissipation channel for the large scales in the sense of classical eddy viscosity. We show that the energy transfer rate depends on the large-scale flow state, which establishes a direct coupling between the large scales and smaller-scale flow features such as small-scale intermittency. [Preview Abstract] |
Saturday, November 23, 2019 5:58PM - 6:11PM |
B28.00007: Energy flux vectors in two-dimensional anisotropic turbulence Masanori Takaoka, Naoto Yokoyama, Eiichi Sasaki Identification of energy flow in the Fourier space is one of the most important problem in turbulence research. In isotropic turbulence, owing to its symmetry, energy flow is one-dimensionalized and treated as scalar. To investigate anisotropic turbulence, on the other hand, it is indispensable to understand its energy flux as a vector field. Although it is required to determine energy budget among three wave modes constituting a triad, solution cannot be determined uniquely. Our idea here is to obtain a flow of energy in the Fourier space similar to the energy cascade in isotropic turbulence. To solve the continuity equation for enrgy flow, we have proposed two idea: use of the Moore-Penrose inverse matrix and potential flux vector. In this talk, we will report the results for the application of our idea to two-dimensional anisotropic turbulence. The Rhines "lazy eight" spectrum in $\beta$-plane turbulence is one of the most conspicuous anisotropy. Charney-Hasegawa-Mima equation and Hasegawa-Wakatani equation in plasma physics also have similar anisotropic term. We have simulated these equations to calculate energy changing rate at each wave number, and then apply our idea to obtain the energy flux vectors in the Fourier space. [Preview Abstract] |
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