Bulletin of the American Physical Society
69th Annual Meeting of the APS Division of Fluid Dynamics
Volume 61, Number 20
Sunday–Tuesday, November 20–22, 2016; Portland, Oregon
Session H35: Turbulence: Theory |
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Chair: Laurent Chevillard, Laboratoire de Physique de l'ENS Lyon Room: Oregon Ballroom 204 |
Monday, November 21, 2016 10:40AM - 10:53AM |
H35.00001: A dissipative random velocity field for fully developed fluid turbulence Laurent Chevillard, Rodrigo Pereira, Christophe Garban We investigate the statistical properties, based on numerical simulations and analytical calculations, of a recently proposed stochastic model for the velocity field of an incompressible, homogeneous, isotropic and fully developed turbulent flow. A key step in the construction of this model is the introduction of some aspects of the vorticity stretching mechanism that governs the dynamics of fluid particles along their trajectory. An additional further phenomenological step aimed at including the long range correlated nature of turbulence makes this model depending on a single free parameter that can be estimated from experimental measurements. We confirm the realism of the model regarding the geometry of the velocity gradient tensor, the power-law behaviour of the moments of velocity increments, including the intermittent corrections, and the existence of energy transfers across scales. We quantify the dependence of these basic properties of turbulent flows on the free parameter and derive analytically the spectrum of exponents of the structure functions in a simplified non dissipative case. A perturbative expansion shows that energy transfers indeed take place, justifying the dissipative nature of this random field. [Preview Abstract] |
Monday, November 21, 2016 10:53AM - 11:06AM |
H35.00002: Dissipation in non-equilibrium turbulence Wouter Bos, Robert Rubinstein For about a decade, experimental and numerical studies have reported on the existence of an anomalous behaviour of the viscous dissipation rate in unsteady turbulence (see for instance Vassilicos, Annu. Rev. Fluid Mech. 2015). It appears that the short-time transient dynamics can be described by a universal power law, incompatible with Taylor's 1935 dissipation rate estimate. We show that these results can be explained using a non-equilibrium energy distribution, obtained from a low-frequency perturbative expansion of simple spectral closure. The resulting description is fairly simple. In particular, during the transient, according to the predictions, the normalized dissipation rate $C_\epsilon$ evolves as a function of the Taylor-scale Reynolds number $R_\lambda$ following the relation $C_\epsilon\sim R_\lambda^{-15/14}$, in close agreement with experimental and numerical observations. [Preview Abstract] |
Monday, November 21, 2016 11:06AM - 11:19AM |
H35.00003: A Lagrangian fluctuation-dissipation relation for scalar turbulence Theodore Drivas, Gregory Eyink An exact relation is derived between the dissipation of scalar fluctuations and the variance of the scalar inputs (due to initial scalar values, scalar sources, and boundary fluxes) as those are sampled by stochastic Lagrangian trajectories. Previous work on the Kraichnan (1968) model of turbulent scalar advection has shown that anomalous scalar dissipation, non-vanishing in the limit of vanishing viscosity and diffusivity, is in that model due to Lagrangian spontaneous stochasticity, or non-determinism of the Lagrangian particle trajectories in the limit. We here extend this result to scalars advected by any incompressible velocity field. For fluid flows in domains without walls (e.g. periodic boxes) and for insulating/impermeable walls with zero scalar fluxes, we prove that anomalous scalar dissipation and spontaneous stochasticity are completely equivalent. For flows with imposed scalar values or non-vanishing scalar fluxes at the walls, spontaneous stochasticity still implies anomalous scalar dissipation but simple examples show that a distinct mechanism of non-vanishing dissipation can be thin scalar boundary layers near the walls. As an example, we consider turbulent Rayleigh-Benard convection. We here obtain an exact relation between steady-state thermal dissipation and the time for diffusive tracer particles released at the top or bottom wall to mix to their final uniform value near those walls. We show that an "ultimate regime" of turbulent convection as predicted by Kraichnan (1962) will occur at high Rayleigh numbers, unless this near-wall mixing time is asymptotically much longer than the large-scale circulation time. [Preview Abstract] |
Monday, November 21, 2016 11:19AM - 11:32AM |
H35.00004: A new approach to Lagrangian investigations of isotropic turbulence Manuel Barjona, Carlos B. da Silva A new numerical approach is used in conjunction with direct numerical simulations (DNS) of statistically stationary (forced) isotropic turbulence to investigate the high Reynolds number scaling properties of turbulence characteristics in a Lagrangian frame. The new method provides an alternative route to the determination of the classical Lagrangian turbulence quantities, such as the second order Lagrangian velocity structure function and two point particle separation, at a much higher Reynolds number than as obtained in previous numerical simulations, and displays excellent agreement with the classical theoretical predictions and existing numerical simulations and experimental data. [Preview Abstract] |
Monday, November 21, 2016 11:32AM - 11:45AM |
H35.00005: Multi-Scale Analysis of Lagrangian Properties of Turbulence Michael Wilczek, Cristian Lalescu Turbulence is a multi-scale problem in space and time with a broad range of strongly interacting degrees of freedom. Lagrangian tracer particles advected with the flow sample this spatio-temporal complexity. This naturally leads to the question of how Lagrangian properties are affected by the scales of turbulence. We attempt to answer this question numerically and theoretically adopting a coarse-graining approach. In an extensive DNS (direct numerical simulation) study, we track tracer particles advected by spatially coarse-grained velocity fields. This allows to distinguish the impact of large-scale sweeping effects and small-scale intermittency on Lagrangian aspects of turbulence. In this presentation we will present results on Lagrangian particle dispersion and velocity fluctuations for various coarse-graining scales. The results will furthermore be discussed in the context of Eulerian-Lagrangian bridging relations. [Preview Abstract] |
Monday, November 21, 2016 11:45AM - 11:58AM |
H35.00006: Turbulence screening suppresses long-range pressure contributions Dimitar Vlaykov, Michael Wilczek The complexity in turbulence can be seen to stem from the non-linearity and non-locality of the governing Navier-Stokes equations. The non-linearity gives rise to structures on many scales with varying topologies -- from strain sheets to vortex tubes. In incompressible flows, these structures determine the pressure field through a Poisson relation. This in turn describes the non-locality of incompressible flows -- formally the pressure at any point is determined by the competition of strain and enstrophy over the entire flow. We show how due to the relative compactness and close proximity of extreme strain and vortex regions a type of effective turbulence screening emerges. We characterize this effect in statistically stationary homogeneous and isotropic turbulence by considering the spatial (two-point) statistics of the velocity gradient fields. This clarifies the observation from both experiments and numerical simulations that a relatively small neighbourhood -- comparable with the small turbulence scales, contains the large majority of the information about the pressure at a given point. We characterize the properties of this neighbourhood as a function of global flow parameters, like Reynolds number, as well as local flow properties, e.g. local topology and dissipation. [Preview Abstract] |
Monday, November 21, 2016 11:58AM - 12:11PM |
H35.00007: Leith diffusion model for homogeneous anisotropic turbulence Robert Rubinstein, Timothy Clark, Susan Kurien A new spectral closure model for homogeneous anisotropic turbulence is proposed. The systematic development begins by closing the third-order correlation describing nonlinear interactions by an anisotropic generalization of the Leith diffusion model for isotropic turbulence. The correlation tensor is then decomposed into a tensorially isotropic part, or directional anisotropy, and a trace-free remainder, or polarization anisotropy. The directional and polarization components are then decomposed using irreducible representations of the SO(3) symmetry group. Under the ansatz that the decomposition is truncated at quadratic order, evolution equations are derived for the directional and polarization pieces of the correlation tensor. Numerical simulation of the model equations for a freely decaying anisotropic flow illustrate the non-trivial effects of spectral dependencies on the different return-to-isotropy rates of the directional and polarization contributions. [Preview Abstract] |
Monday, November 21, 2016 12:11PM - 12:24PM |
H35.00008: A generalized four-fifth law for compressible turbulence Hussein Aluie Kolmogorov's 4/5-th law is a celebrated exact result of incompressible turbulence, and is key to the formulation of his 1941 phenomenology. We will present its generalization to compressible turbulence. [Preview Abstract] |
Monday, November 21, 2016 12:24PM - 12:37PM |
H35.00009: The structure of the extreme Lyapunov exponents in the inertial scales of turbulence Alberto Vela-Martin, Javier Jimenez A fully reversible homogeneous isotropic turbulent system is constructed using inviscid LES to model energy fluxes in the far inertial range. Reversibility is exploited to efficiently calculate the highest/most unstable and lowest/most stable short-time Lyapunov exponents (STLE) of the system. When restricted to inertial modes, both extreme STLE have similar absolute value and inverse sign, suggesting the Hamiltonian nature of inertial dynamics. Their associated short-time Lyapunov vectors (STLV), which are complete flow fields that provide information on the perturbations to which the system is most/least sensitive, are found to be concentrated in small regions in physical space. The analysis of the structure of the STLV reveals that these small regions, where intense expansive and contractive events take place, are strongly dominated by the strain field of the flow. These regions are also characterized by a preferential alignment of the field of the STLV with the different eigenvectors of the strain tensor. However, no strong correlation of the STLV with the vorticity field is found. These results emphasize the active role of the strain in turbulence dynamics. [Preview Abstract] |
Monday, November 21, 2016 12:37PM - 12:50PM |
H35.00010: Analytic prediction for planar turbulent boundary layers Zhen-Su She, Xi Chen Analytic predictions of mean velocity profile (MVP) and streamwise ($x)$ development of related integral quantities are presented for flows in channel and turbulent boundary layer (TBL), based on a symmetry analysis of eddy length and total stress. Specific predictions include the relations for momentum Reynolds number ($Re_{\theta } )$ with friction $Re_{\tau } $ and streamwise $Re_{x} $:$Re_{\theta } \approx 3.27Re_{\tau } $ and$Re_{x} /Re_{\theta } =4.94[(\ln \mbox{Re}_{\theta } +1.88)^{2}+1]$; the streamwise development of the friction velocity$u_{\tau } $: $U_{e} /u_{\tau } \approx 2.22\ln Re_{x} +2.86-3.83\ln (\ln Re_{x} )$, and of the boundary layer thickness $\delta_{e} $:$x/\delta_{e} \approx 7.27\ln Re_{x} -5.18-12.52\ln (\ln Re_{x} )$, which are fully validated by recent reliable data. [Preview Abstract] |
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