Energy Cascade in Large-Eddy Simulations of Turbulent Fluid Flows

In field experiments designed to study subgrid-scale parameterizations for large eddy simulation, the flow field is often measured and then filtered in two-dimensional planes. This two-dimensional filtering serves as a surrogate for three-dimensional filtering. The question of whether this will yield accurate results in subgrid-scale (SGS) models is addressed by analyzing data from a field experiment in which 16 sonic anemometers were deployed in a four by four grid. The experiment was held in July 2002 at the Surface Layer Turbulence and Environmental Science Test (SLTEST) facility in the Utah West Desert. The full SGS stress tensor and its parameterizations using both two-and three-dimensional filterings are obtained. Comparisons are given between two-and three-dimensional filterings of the field measurements based on probability density functions (PDFs) and energy spectra of the SGS stress elements. The PDFs reveal that quantities calculated with two-dimensional filtering exhibit greater intermittency than those computed with three-dimensional filtering at the same scale. From the spectra it is observed that the different filtering methods result in similar behavior, but that spectra of SGS stress components computed with a threedimensional filter roll off at a slightly lower wavenumber than those computed with a two-dimensional filter. The PDFs and spectra of the stresses calculated with two-and three-dimensional filters can be made to collapse by reducing the three-dimensional filter scale according to ⌬ 3ϪD ϭ 0.84⌬ 2ϪD . Geometric alignment analyses are performed for the SGS heat flux, SGS stress, and filtered strain rate for the cases of stable, near-neutral, and unstable atmospheric stabilities. Under unstable and near-neutral atmospheric stability, two-dimensional filtering yields acceptable results; however, under stable atmospheric stability, a new approach is recommended and delineated.

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“…The tensor eddy diffusivity (or nonlinear) model (Leonard 1974;Borue and Orszag 1998) is given by ← FIG. 5.…”

Section: Sgs Heat Flux Alignmentsmentioning

confidence: 99%

“…This can be shown mathematically (Leonard 1997) by keeping the first term in an expansion of the filtered product Tu ĩ that appears in the definition of q. A third approach, the so-called mixed model (Bardina and Ferziger 1980), is a linear combination of Eqs.…”

Section: Sgs Heat Flux Alignmentsmentioning

confidence: 99%

The Effect of Filter Dimension on the Subgrid-Scale Stress, Heat Flux, and Tensor Alignments in the Atmospheric Surface Layer

Higgins

Meneveau

Parlange

2007

Journal of Atmospheric and Oceanic Technology

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“…In the present work, we apply a line of reasoning that is motivated by the tensor diffusivity model for LES (e.g., [17,18]). This model uses a Taylor series expansion of the filtered product of two arbitrary functions, f and h,…”

Section: Filteringmentioning

confidence: 99%

A Super-Grid-Scale Model for Simulating Compressible Flow on Unbounded Domains

Colonius¹,

Ran

2002

Journal of Computational Physics

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A new buffer region (absorbing layer, sponge layer, fringe region) technique for computing compressible flows on unbounded domains is proposed. We exploit the connection between coordinate mapping from bounded to unbounded domains and filtering of the equations of motion in Fourier space in order to develop a model to damp flow disturbances (advective and acoustic) that propagate outside an arbitrarily defined near field. This effectively simulates a free-space boundary condition. Damping the solution in the far field is accomplished in a simple and effective way by applying a filter (similar to that used in large-eddy simulation) on a mesh in Fourier space, followed by a secondary filtering of the equations on the physical grid and implementation of a model for the unresolved scales. The final form of the buffer region is given in real space, independent of any discretization of the equations. Here we use a dealiased, Fourier spectral collocation method to demonstrate the efficacy of the buffer region for several model problems: acoustic wave propagation, convection of a finite-amplitude vortex, and a viscous starting jet in two dimensions. The results compare favorably to previous nonreflecting and absorbing boundary conditions.

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“…In large-eddy simulations, the velocity field is separated into a resolved (large-scale) and a subgrid (small-scale) field, by a spatial filtering operation (Leonard 1974). The non-dimensional continuity and Navier-Stokes equations for the resolved velocity field are @u…”

Section: Problem Formulationmentioning

confidence: 99%

Large-eddy simulation of three-dimensional dunes in a steady, unidirectional flow. Part 2. Flow structures

Omidyeganeh

Piomelli

2013

J. Fluid Mech.

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This is the accepted version of the paper.This version of the publication may differ from the final published version. We performed large-eddy simulations of the flow over a series of three-dimensional (3D) dunes at laboratory scale. The bedform three-dimensionality was imposed by shifting a standard two-dimensional (2D) dune shape in the streamwise direction according to a sine wave. The turbulence statistics were discussed in Part 1 of this article [M. Omidyeganeh, U. Piomelli, J. Fluid Mech. 721, pp. 454-483, (2013)]. Coherent flow structures and their statistics are discussed concentrating on two cases with the same crestline amplitudes and wavelengths but di↵erent crestline alignments: in-phase and staggered. The present paper shows that the induced large-scale mean streamwise vortices are the primary factor that alters the features of the instantaneous flow structures. Wall turbulence is insensitive to the crestline alignment; alternating high-and low-speed streaks appear in the internal boundary layer developing on the stoss side, whereas over the node plane (the plane normal to the spanwise direction at the node of the crestline), they are inclined towards the lobe plane (the plane normal to the spanwise direction at the most downstream point of the crestline) due to the mean spanwise pressure gradient. Spanwise vortices (rollers) generated by Kelvin-Helmholtz instability in the separated shear-layer appear regularly over the lobe with much larger length scale than those over the saddle (the plane normal to the spanwise direction at the most upstream point of the crestline). Rollers over the lobe may extend to the saddle plane and a↵ect the reattachment features; their shedding is more frequent than in 2D geometries. Vortices shed from the separated shear-layer in the lobe plane undergo a three-dimensional instability while advected downstream, and rise toward the free surface. They develop into a horseshoe shape (similar to the 2D case) and a↵ect the whole channel depth, whereas those generated near the saddle are advected downstream and toward the bed. When the tip of such a horseshoe reaches the free surface, the ejection of flow at the surface causes "boils" (upwelling events on the surface). Strong boil events are observed on the surface of the lobe planes of 3D dunes more frequently than in the saddle planes. They also appear more frequently than in the corresponding 2D geometry. The crestline alignment of the dune alters the dynamics of the flow structures, in that they appear in the lobe plane and are advected towards the saddle plane of the next dune, where they are dissipated. Boil events occur at a higher frequency in the staggered alignment, but with less intensity than in the in-phase alignment. Permanent repository link

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Energy Cascade in Large-Eddy Simulations of Turbulent Fluid Flows

Cited by 899 publications

References 9 publications

The Effect of Filter Dimension on the Subgrid-Scale Stress, Heat Flux, and Tensor Alignments in the Atmospheric Surface Layer

The Effect of Filter Dimension on the Subgrid-Scale Stress, Heat Flux, and Tensor Alignments in the Atmospheric Surface Layer

A Super-Grid-Scale Model for Simulating Compressible Flow on Unbounded Domains

Large-eddy simulation of three-dimensional dunes in a steady, unidirectional flow. Part 2. Flow structures

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