Bulletin of the American Physical Society
74th Annual Meeting of the APS Division of Fluid Dynamics
Volume 66, Number 17
Sunday–Tuesday, November 21–23, 2021; Phoenix Convention Center, Phoenix, Arizona
Session P04: Turbulence Theory |
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Chair: Robert Moser, UT Austin Room: North 121 B |
Monday, November 22, 2021 4:05PM - 4:18PM |
P04.00001: Role of Large-Scale Forcing on Velocity Gradient Dynamics in Turbulence Rishita Das, Sharath S Girimaji This work highlights the profound role of forcing in small-scale velocity-gradient (VG) dynamics. Specifically, we seek to explain the interactions among forcing, inertial, pressure, and viscous effects leading to the observed small-scale behavior. Data from direct numerical simulations of isotropic and anisotropic incompressible turbulence is used to examine the effect of forcing on the evolution of VG invariants, Q and R. It is demonstrated that forcing, opposes inertial and viscous action in the strain-dominated nodal topologies and it counteracts the non-local pressure in rotation-dominated unstable focal topologies. The most important contribution of forcing is to balance the dilatational probability current of the combined inertial-pressure-viscous action. To a significant extent, the solenoidal probability current of inertial-pressure-viscous action, drives the overall VG dynamics. These findings have important implications in the development of stochastic VG models. |
Monday, November 22, 2021 4:18PM - 4:31PM |
P04.00002: Vortex Gas Model of Turbulent Circulation Statistics and Truncated Scalar Fields Gabriel Brito Apolinário, Luca Moriconi, Rodrigo Miranda Pereira, Victor de Jesus Valadão Statistical properties of circulation — a fluid dynamic observable which shares mathematical properties with the Wilson Loop operator of gauge field theories — encode relevant information about the multi-scale structure of turbulent cascades. Recent massive computational efforts have brought to light the dependence of circulation moments upon Reynolds numbers and length scales, besides the specific shape of heavy-tailed circulation probability distribution functions. We address these focal points in an investigation of circulation statistics for planar cuts of three-dimensional flows. We borrow ideas from the structural approach to turbulence, whereby turbulent flows are depicted as dilute vortex gases, combined with the standard Obukhov-Kolmogorov phenomenological framework of small-scale intermittency. A refinement of our model takes us to the phenomenon of multifractality breaking, which we propose to describe with the help of truncated two-dimensional scalar fields. It is possible to reproduce, along these lines, key statistical features of circulation, in close agreement with empirical observations compiled from direct numerical simulations. |
Monday, November 22, 2021 4:31PM - 4:44PM |
P04.00003: Anisotropic Redistribution of Turbulent Kinetic Energy in the Troposphere Charles A Petty, Andre Bernard A coupling between the velocity field and the Coriolis field in the troposphere can redistribute kinetic energy at very small scales even if the mean turbulent field is spatially homogeneous. The purpose of this presentation is to define a model for the Reynolds stress that provides a closure for the Reynolds Averaged Navier-Stokes equation for all inertial and non-inertial temporal frames-of-reference. Mixing and production of the turbulent kinetic energy and the turbulent dissipation depend on the Reynolds stress and the Cauchy stress. It is noteworthy that the Coriolis Theorem predicts that the strain rate is frame insensitive; and, that the Reynolds stress is frame sensitive. Consequently, the Cauchy stress and the Reynolds stress are not similar. This presentation will illustrate that the URAPS-closure for the Reynolds stress (see Koppula et al.,2009,Chem. Eng. Sci. 64,4611-4624; 2011,Ind.Eng.Chem.Res.,50(15),8905-8916; 2013,Physica Scripta,T155) predicts that the turbulent dispersion and the turbulent dissipation of kinetic energy are positive; and, that the "production" of kinetic energy could be either positive or negative. For homogeneous decay, anisotropic mixing of kinetic energy could produce hue differences in the sky. This phenomena may explain how foraging birds are able to return to their natal nest with fidelity. |
Monday, November 22, 2021 4:44PM - 4:57PM |
P04.00004: The approach to Kolmogorov equilibrium Konstantinos Steiros At the limit of infinite Reynolds number, the K41 framework yields, asymptotically, the -5/3 law for the inertial subrange of turbulence. The latter is assumed to be in equilibrium. However, in non-stationary conditions (e.g. decaying turbulence) a large portion of the cascade will not be in equilibrium, even when the Reynolds number is extremely large. There, the -5/3 law is expected not to be exact. This work proposes a correction to the -5/3 law for scales which are not in exact equilibrium. The correction becomes asymptotically negligible when the Reynolds number tends to infinity, and for scales which are of negligible size compared to the integral length scale, in agreement with K41. A link between the K41 framework and the k-epsilon model of turbulence is also proposed. Experimental (grid turbulence) and numerical (DNS) evidence are provided in support of the proposed theoretical predictions. |
Monday, November 22, 2021 4:57PM - 5:10PM |
P04.00005: Scale-Dependent Geometric Statistics of Homogeneous Turbulent Shear Flow Frank G Jacobitz, Kai Schneider Scale-dependent geometrical statistics are introduced in order to consider the alignment properties of different vector-valued flow quantities. The vector fields are developed into an orthogonal wavelet series and the angle of the scale-wise contributions of different vector quantities, which are mutually orthogonal, can thus be quantified. This allows us to revisit Taylor's random hypothesis by examining the cancellation properties of Eulerian and convective accelerations at different flow scales, which is motivated by the authors' recent work in Phys. Rev. Fluids, 6, 074609, 2021. The obtained results for homogeneous turbulent shear flow, computed by direct numerical simulation, support that Taylor's hypothesis holds at small scales of the flow, reflected by the anti-alignment of the Eulerian acceleration and the convective term. |
Monday, November 22, 2021 5:10PM - 5:23PM |
P04.00006: Markov properties of velocity increments in turbulent channel flow Sheldon Harrison, Samuel D Lortie, Laurent B Mydlarski It has been established that statistics of turbulent velocity increments can be modelled using Markov processes if the increments are measured over separations greater than the Taylor microscale, and that the PDFs of such increments can be described by a Fokker-Planck equation if the higher-order terms of the Kramers-Moyal (K-M) expansion are small (Renner, Peinke & Friedrich, J. Fluid Mech., 2001). The present work builds on that of Tutkun (Physica D, 2017), who demonstrated that the minimum separation at which a turbulent boundary layer exhibits Markovian properties depends on the wall-normal distance. However, the magnitude of the higher-order terms of the K-M expansion and the ensuing applicability of a Fokker-Planck equation to the modelling of velocity increments in wall-bounded turbulence has yet to be investigated. To this end, the present work examines the dependence of statistics of velocity increments on their wall-normal position by way of hot-wire measurements in a turbulent channel flow. It is i) confirmed that the degree to which the turbulent channel flow can be accurately modelled as Markovian also depends on the distance from the wall, and ii) demonstrated that the higher-order terms become increasingly important as the wall is approached. |
Monday, November 22, 2021 5:23PM - 5:36PM |
P04.00007: Dynamical Fractional and Multifractal Fields Gabriel B Apolinário, Laurent Chevillard, Jean-Christophe Mourrat Motivated by the modeling of three-dimensional fluid turbulence, we study a stochastic partial differential equation (SPDE) that is randomly stirred by a spatially smooth and uncorrelated in time forcing term. This dynamical evolution includes a linear but nonlocal interaction which is responsible for a cascading transfer of energy towards smaller scales. In the linear and Gaussian framework, the solution develops fractional regularity, for which we derive explicit predictions for the statistical behavior. Intermittency corrections are included drawing inspiration from a known probabilistic model, the Gaussian multiplicative chaos, which motivates the introduction of a quadratic interaction in this model. Through numerical simulations, we observe the non-Gaussian and in particular skewed nature of these solutions, an important feature in the modeling of turbulent velocity fields. |
Monday, November 22, 2021 5:36PM - 5:49PM |
P04.00008: Discretization induced statistical artifacts in large-eddy simulation Gopal R Yalla, Robert Moser, Todd Oliver Two effects of numerical discretization on the statistical properties of large-eddy simulation (LES) are discussed. First, we demonstrate the impact of numerical dispersion error on the energy cascade in LES. It is shown that dispersion error causes a phase decoherence between triad interacting wavemodes, leading to a reduction in the mean energy transfer rate for these scales and a corresponding reduction in the energy spectrum. The second result concerns the commutator between the filtering and differentiation operators, which arises as a result of inhomogeneous filtering/resolution in a LES. A statistical description of the commutator is derived for a general filter in terms of the energy spectrum, which can serve as a target for commutation models and determines the importance of the commutator relative to other turbulent processes. Both issues are explored through multiscale asymptotic analyses and simulations of homogeneous isotropic turbulence. |
Monday, November 22, 2021 5:49PM - 6:02PM |
P04.00009: Lagrangian gradient transport for variable-density turbulence G S Sidharth, J R Ristorcelli We apply Lagrangian analysis to materially conserved scalars for turbulent transport in variable-density flows. The consequences of the material conservation of density leads to meaningfully different expressions for the turbulent transport. Formal Lagrangian analysis produces gradient transport expressions substantially different from those obtained by the physically intuitive “argument by analogy” method used in computational models. These intuitive arguments, in Favre and Reynolds averaged settings, are contrasted to the formal Lagrangian results. It is shown that the basis functions of gradient transport theory are different when there is an additional materially conserved variable. In variable density flows, the turbulent fluxes now depend on the mean density gradient indicating the possibility of counter gradient transport from first principles as seen in some laboratory experiments. Using expressions from the formal analysis, we derive consistent gradient transport expressions for the turbulent transport terms that appear in the first- and second-order Favre moment equations. It is shown that arguments by analogy from constant density transport for the Favre fluxes are not consistent with the Lagrangian results. The analysis is limited to transport by high Reynolds number turbulent fluctuations in the presence of mean gradients and negligible dilatation of the fluctuating velocity. The results are applicable to turbulent combustion and to stellar convection problems in which the density fluctuations are on the order of the mean density. |
Monday, November 22, 2021 6:02PM - 6:15PM |
P04.00010: Wave turbulence on rational and irrational tori Yulin Pan, Alexander A Hrabski, Gigliola Staffilani, Bobby Wilson We study wave turbulence in the nonlinear Schrödinger equation on two-dimensional domains of rational and irrational aspect ratios (i.e. rational and irrational tori). Situations with and without high-frequency dissipation are considered. For the former, we numerically study the quasi-stationary power-law spectra and energy cascades. We show that these quantities are remarkably different on the two tori, with reasons explained in terms of the discrete resonant manifold. For the latter, the focus is on the migration of initial data to high frequencies measured by the Sobolev norm. We will review the study of the problem in the harmonic analysis community, and discuss our new mathematical proof on the existence of a barrier to the energy cascade on irrational tori, followed by numerical demonstrations. The results in this work have important implications in understanding simulations of wave turbulence in periodic domains. |
Monday, November 22, 2021 6:15PM - 6:28PM |
P04.00011: Exact decomposition of energy and helicity fluxes in (magneto-)hydrodynamic turbulence Moritz F Linkmann, Perry L Johnson, Sean Oughton, Luca Biferale Recently, an exact decomposition of the energy flux from large to small scales in three-dimensional turbulence into contributions associated with vortex stretching and strain self-amplification has been derived (P. Johnson, Phys. Rev. Lett., 124, 104501 (2020)). Applied to data from direct numerical simulations, this decomposition results in a quantification of the relative contributions of the respective terms to the energy cascade. |
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