Bulletin of the American Physical Society
77th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 24–26, 2024; Salt Lake City, Utah
Session A40: Turbulence Theory |
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Chair: Frank Jacobitz, University of San Diego Room: 355 F |
Sunday, November 24, 2024 8:00AM - 8:13AM |
A40.00001: A Scale-Dependent Analysis of the Return to Isotropy from Anisotropic Homogeneous Turbulent Shear Flow Frank G Jacobitz, Kai Schneider Using results obtained from direct numerical simulations, the current work studies the return to isotropy from anisotropic homogeneous turbulent shear flow as well as from imposed polarization anisotropy. A wavelet-based scale-dependent decomposition of the velocity fields is performed and the Reynolds stress anisotropy tensor is used to quantify the anisotropy features of the total flow fields as well as the fields at different scales of the turbulent motion. In the case of homogeneous turbulent shear flow, the larger scales of the turbulent motion contribute more strongly to the anisotropy of the flow, but even the smaller scales hold lower levels of anisotropy. The return towards isotropy from anisotropic states due to shear and polarization anisotropy is most pronounced at the smallest scales of the turbulent motion, while anisotropy remains present for multiple eddy-turnover time scales at the larger scales of the turbulent motion. |
Sunday, November 24, 2024 8:13AM - 8:26AM |
A40.00002: Corrections for higher-order spectral estimates of Gaussian processes Clayton Byers, Kelly Y Huang, Matthew K Fu A common assumption utilized in turbulence theory is the tendency towards Gaussian statistics for streamwise velocity fluctuations. The analytical expressions associated with the probability distribution functions and statistics that yield from a Gaussian process allow for simplifications in turbulence theories, especially with respect to higher order statistics of velocity fluctuations. In the case of the Random Sweeping Decorrelation Hypothesis, the assumption of Gaussian statistics allows an estimate of the higher-order spectral content, and thus higher-order moments, of the streamwise velocity fluctuations solely from the first-order spectrum. However, most real flows do not follow a normal distribution across all scales, and therefore will depart from these idealized behaviors. Deviations in the spectral content from the ideal Gaussian behavior are investigated with phase randomized turbulence with varying levels of skewness and kurtosis. It is found that combinations of non-zero skewness and sub-gaussian kurtosis combine to compensate for each other, resulting in Gaussian approximations of higher-order moments nearly equating to actual moment calculations. The resulting implications on the Random Sweeping Decorrelation Hypothesis, including both spectral estimates and the logarithmic scaling of the moments, are discussed. |
Sunday, November 24, 2024 8:26AM - 8:39AM |
A40.00003: Searching for hidden symmetry in passive scalar advected by 2D Navier-Stokes turbulence Chiara Calascibetta, Luca Biferale, Fabio Bonaccorso, Massimo Cencini, Alexei A Mailybaev The statistical behavior of a scalar passively advected by a Navier-Stokes flow resulting from a two-dimensional inverse energy cascade is strongly intermittent, displaying anomalous multiscaling [1], which violates Kolmogorov's self-similarity predictions. Recently, the concept of hidden symmetry has been introduced to define a new set of dynamically rescaled (projected) variables for which scale invariance is restored and allowing to calculate from the projected equation of motion the anomalous scaling of the structure functions. Hidden symmetry has been numerically validated in the context of the shell models [2,3]. In this work we scrutinize its validity for the case of the passive scalar by inspecting the probability distribution function of multipliers, obtained as the ratio of suitably defined scalar increments at two different inertial scales [4]. We also verify the Perron-Frobenius scenario for the anomalous scaling law of structure functions as a consequence of the hidden symmetry. |
Sunday, November 24, 2024 8:39AM - 8:52AM |
A40.00004: Probability density functions of enstrophy and energy dissipation rate and their 1D surrogates in incompressible isotropic turbulence Toshiyuki Gotoh, P.K. Yeung Relation between the probability density functions (PDFs) of the three dimensional (3D) enstrophy and the one dimensional (1D) enstrophy surrogate in the incompressible isotropic turbulence is theoretically derived and verified by the direct numerical simulations. The relation indicates that the PDF of the 1D surrogate enstrophy has the longer tail than that of the PDF of 3D enstrophy and that their long tails are the stretched exponential with the same stretching exponents. Similar results for the PDFs of the 3D dissipation rate and the 1D dissipation surrogate are obtained and numerically verified. It is shown that the ratio of the moments of 3D dissipation to that of the 1D surrogate grows rapidly with the order but is independent of the Reynolds number. |
Sunday, November 24, 2024 8:52AM - 9:05AM |
A40.00005: Time-dependent viscosity, dissipation, and the turbulent cascade Daniel M. Israel Rapid changes to the mean temperature result in corresponding changes in the molecular viscosity. The viscosity, in turn, will effect the dissipation rate, throwing the turbulence out of equilibrium, and requiring a subsequent relaxation back to an equilibrium state. This is an important process in numerous engineering problems, including internal combustion engines (heating due to compression and combustion) and turbulence passing through a shock. Using direct-numerical simulation of incompressible turbulence with a time-dependent viscosity, we can observe the effect of both the initial viscosity change and the subsequent return to equilibrium. Considering both the spectra and higher-order statistics we can identify some key issues for future model improvements. |
Sunday, November 24, 2024 9:05AM - 9:18AM |
A40.00006: Contour Shape Dependency of Circulation Statistics in Homogeneous and Isotropic Turbulence Luca Moriconi, Kartik P Iyer Statistical moments of the turbulent circulation are complex geometry-dependent functionals of closed oriented contours and present a hard challenge for theoretical understanding. Conveniently defined circulation moment ratios, however, are empirically known to have appreciable geometric dependency only at lower moment orders and for contours which are sized near the bottom of the inertial range, in the situation where they span minimal surfaces of equivalent areas. Resorting to ideas addressed in the framework of the vortex gas model of circulation statistics, which integrates structural and multifractal aspects of the turbulent velocity field, we are able to reproduce, with reasonable accuracy, the observed contour shape dependency of circulation moment ratios, up to high order statistics. A key phenomenological point in our discussion is the assumption that the energy dissipation field, closely related to the local density of thin vortex tubes, is sharply bounded from above at finite Reynolds numbers. |
Sunday, November 24, 2024 9:18AM - 9:31AM |
A40.00007: Abstract Withdrawn
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Sunday, November 24, 2024 9:31AM - 9:44AM |
A40.00008: Departure from the statistical equilibrium of large scales in three-dimensional hydrodynamic turbulence Jin-Han Xie, Mengjie Ding, Jianchun Wang We study the statistically steady states of the forced dissipative three-dimensional homogeneous isotropic turbulence at scales larger than the forcing scale in real separation space. The probability density functions (PDFs) of longitudinal velocity difference at large separations are close to but deviate from Gaussian, measured by their non-zero odd parts. We propose a conjugate regime to Kolmogorov's inertial range, independent of the forcing scale, to capture the odd parts of PDFs. The analytical expressions of the third-order longitudinal structure functions derived from the K\'arm\'an-Howarth-Monin equation prove that the odd-part PDFs of velocity differences at large separations are non-zero and show that the odd-order longitudinal structure functions have a universal power-law decay as the separation tends to infinity regardless of the particular forcing form, implying a strong coupling between large and small scales. Similar behaviour is also found for the large-scale dynamics of passive scalars. |
Sunday, November 24, 2024 9:44AM - 9:57AM |
A40.00009: Ensemble decomposition for Lagrangian turbulence: Reynolds number trends and modeling Lukas Bentkamp, Rohini Uma-Vaideswaran, Cristian C Lalescu, P.K Yeung, Michael Wilczek Previous work (Bentkamp et al. Nat. Commun. 10:3550, 2019) has shown that Lagrangian statistics in homogeneous isotropic turbulence can be approximately decomposed into Gaussian sub-ensembles by considering statistics conditioned on the squared acceleration coarse-grained over a viscous time scale. In this framework, each sub-ensemble is determined by the conditional Lagrangian velocity autocorrelation function. Using high-fidelity direct numerical simulation (DNS) data, we here explore Reynolds-number trends of the conditional correlation functions. Our evaluation shows that, for short times, the conditional correlation functions can be approximately collapsed for different Reynolds numbers by appropriate rescaling, enabling modeling approaches across Reynolds numbers. We present results on such a model along with comparisons to DNS data. |
Sunday, November 24, 2024 9:57AM - 10:10AM |
A40.00010: Constructing Turbulent Field Statistics with an Ensemble of Multifractal Gaussian Fields Mark Warnecke, Lukas Bentkamp, Gabriel B Apolinário, Michael Wilczek, Perry L Johnson Obtaining field statistics for fluid turbulence remains an outstanding challenge in turbulence theory and modeling. Multifractal models for velocity gradient and increment distributions successfully capture intermittency, but currently do not give easy access to more general multi-point statistics—i.e. field statistics. Here, we present a method that generates field statistics in the form of a characteristic functional by promoting a model for multifractal increment statistics to an ensemble of Gaussian fields. Careful construction of the correlation function and the corresponding weight of each sub-ensemble allows us to define functionals with multifractal two-point inertial statistics, gradient statistics (dissipation range), as well as a large-scale cut-off. Additionally, the method is capable of producing multifractal statistics with any of the widely used singularity spectra (log-normal, She–Lévêque, etc.). |
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