Influence of Subgrid Scales on Resolvable Turbulence and Mixing in Rayleigh-Taylor Flow (original) (raw)
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Subgrid‐scale energy transfer in the near‐wall region of turbulent flows
Physics of Fluids, 1994
Direct numerical simulation databases of turbulent channel and pipe flow have been used in order to assess the energy transfer between resolved and unresolved motions in large-eddy simulations. To this end, the velocity fields are split into three parts: a statistically stationary mean flow, the resolved, and the unresolved turbulent fluctuations. The distinction between the resolved and unresolved motions is based on the application of a cutoff filter in spectral space. Within the buffer layer a backward transfer of averaged kinetic energy from subgrid to grid-scale turbulent motions has been found to exist, which is primarily caused by subgrid-scale stresses aligned with the mean rates of strain. Such reverse transfer generally cannot be described by the simple eddy-viscosity-type subgrid models usually applied in large-eddy simulations. The use of a conditional averaging technique revealed that the reverse transfer of energy within the near-wall flow is strongly enhanced by coherent motions, such as the well-known bursting events.
Journal of Fluid Mechanics, 2000
The dynamics of subgrid-scale energy transfer in turbulence is investigated in a database of a planar turbulent jet at Reλ ≈ 110, obtained by direct numerical simulation. In agreement with analytical predictions (Kraichnan 1976), subgrid-scale energy transfer is found to arise from two effects: one involving non-local interactions between the resolved scales and disparate subgrid scales, the other involving local interactions between the resolved and subgrid scales near the cutoff. The former gives rise to a positive, wavenumber-independent eddy-viscosity distribution in the spectral space, and is manifested as low-intensity, forward transfers of energy in the physical space. The latter gives rise to positive and negative cusps in the spectral eddy-viscosity distribution near the cutoff, and appears as intense and coherent regions of forward and reverse transfer of energy in the physical space. Only a narrow band of subgrid wavenumbers, on the order of a fraction of an octave, make ...
Dynamical modelling of sub-grid scales in 2D turbulence
We develop a new numerical method which treats resolved and sub-grid scales as two different fluid components evolving according to their own dynamical equations. These two fluids are nonlinearly interacting and can be transformed one into another when their scale becomes comparable to the grid size. Equations describing the two-fluid dynamics were rigorously derived from Euler equations [B. Dubrulle, S. Nazarenko, Physica D 110 (1997) 123-138] and they do not involve any adjustable parameters. The main assumption of such a derivation is that the large-scale vortices are so strong that they advect the sub-grid scales as a passive scalar, and the interactions of small scales with small and intermediate scales can be neglected. As a test for our numerical method, we performed numerical simulations of 2D turbulence with a spectral gap, and we found a good agreement with analytical results obtained for this case by Nazarenko and Laval [Non-local 2D turbulence and passive scalars in Batchelor's regime, J. Fluid Mech., in press]. We used the two-fluid method to study three typical problems in 2D dynamics of incompressible fluids: decaying turbulence, vortex merger and forced turbulence. The two-fluid simulations performed on at 128 2 and 256 2 resolution were compared with pseudo-spectral simulations using hyperviscosity performed at the same and at much higher resolution. This comparison shows that performance of the two-fluid method is much better than one of the pseudo-spectral method at the same resolution and comparable computational cost. The most significant improvement is observed in modeling of the small-scale component, so that effective inertial interval increases by about two decades compared to the high-resolution pseudo-spectral method. Using the two-fluid method, we demonstrated that the k −3 tail always exists for the energy spectrum, although its amplitude is slowly decreasing in decaying turbulence.
Dynamical modeling of sub-grid scales in 2D turbulence
Physica D: Nonlinear Phenomena, 2000
We develop a new numerical method which treats resolved and sub-grid scales as two different fluid components evolving according to their own dynamical equations. These two fluids are nonlinearly interacting and can be transformed one into another when their scale becomes comparable to the grid size. Equations describing the two-fluid dynamics were rigorously derived from Euler equations [B. Dubrulle, S. Nazarenko, Physica D 110 (1997) 123-138] and they do not involve any adjustable parameters. The main assumption of such a derivation is that the large-scale vortices are so strong that they advect the sub-grid scales as a passive scalar, and the interactions of small scales with small and intermediate scales can be neglected. As a test for our numerical method, we performed numerical simulations of 2D turbulence with a spectral gap, and we found a good agreement with analytical results obtained for this case by Nazarenko and Laval [Non-local 2D turbulence and passive scalars in Batchelor's regime, J. Fluid Mech., in press]. We used the two-fluid method to study three typical problems in 2D dynamics of incompressible fluids: decaying turbulence, vortex merger and forced turbulence. The two-fluid simulations performed on at 128 2 and 256 2 resolution were compared with pseudo-spectral simulations using hyperviscosity performed at the same and at much higher resolution. This comparison shows that performance of the two-fluid method is much better than one of the pseudo-spectral method at the same resolution and comparable computational cost. The most significant improvement is observed in modeling of the small-scale component, so that effective inertial interval increases by about two decades compared to the high-resolution pseudo-spectral method. Using the two-fluid method, we demonstrated that the k −3 tail always exists for the energy spectrum, although its amplitude is slowly decreasing in decaying turbulence.
The Role of Coherent Structures in Subgrid-Scale Energy Transfer in Turbulent Channel Flow
The present effort documents the relationship between dominant subgrid-scale energy transfer events and coherent motions within the log layer of wall turbulence. Instantaneous velocity fields in the streamwise-wall-normal plane of a zero-pressure-gradient turbulent boundary layer acquired by particle-image velocimetry at Re ϵ u * ␦ / = 2350 are spatially filtered to generate an ensemble of resolved-scale velocity fields in the spirit of large-eddy simulation. The relationship between subgrid-scale dissipation and embedded coherent structures is then studied using instantaneous realizations and conditional averaging techniques. This analysis reveals that strong forward-and backward-scatter events occur spatially coincident to individual hairpin vortices and their larger-scale organization into vortex packets. In particular, large-scale regions of forward scatter are observed along the inclined interface of the packets, coincident with strong ejections induced by the individual vortices. The most intense forward-scatter events are found to occur when these ejections are opposed by sweep motions. Strong backward scatter of energy is observed at the trailing edge of the vortex packets and weaker backscatter is also noted locally around the individual heads of the hairpin structures. The collective observations presented herein demonstrate that hairpin vortices and their organization into larger-scale packets are important contributors to interscale energy transfer in the log layer of wall turbulence.
Physics of Fluids, 2006
The present effort documents the relationship between dominant subgrid-scale energy transfer events and coherent motions within the log layer of wall turbulence. Instantaneous velocity fields in the streamwise-wall-normal plane of a zero-pressure-gradient turbulent boundary layer acquired by particle-image velocimetry at Re ϵ u * ␦ / = 2350 are spatially filtered to generate an ensemble of resolved-scale velocity fields in the spirit of large-eddy simulation. The relationship between subgrid-scale dissipation and embedded coherent structures is then studied using instantaneous realizations and conditional averaging techniques. This analysis reveals that strong forward-and backward-scatter events occur spatially coincident to individual hairpin vortices and their larger-scale organization into vortex packets. In particular, large-scale regions of forward scatter are observed along the inclined interface of the packets, coincident with strong ejections induced by the individual vortices. The most intense forward-scatter events are found to occur when these ejections are opposed by sweep motions. Strong backward scatter of energy is observed at the trailing edge of the vortex packets and weaker backscatter is also noted locally around the individual heads of the hairpin structures. The collective observations presented herein demonstrate that hairpin vortices and their organization into larger-scale packets are important contributors to interscale energy transfer in the log layer of wall turbulence.
Evolution and modelling of subgrid scales during rapid straining of turbulence
Journal of Fluid Mechanics, 1999
The response, evolution, and modelling of subgrid-scale (SGS) stresses during rapid straining of turbulence is studied experimentally. Nearly isotropic turbulence with low mean velocity and Rλ˜290 is generated in a water tank by means of spinning grids. Rapid straining (axisymmetric expansion) is achieved with two disks pushed towards each other at rates that for a while generate a constant strain rate. Time-resolved, two-dimensional velocity measurements are performed using cinematic PIV. The SGS stress is subdivided to a stress due to the mean distortion, a cross-term (the interaction between the mean and turbulence), and the turbulent SGS stress τ(T)ij. Analysis of the time evolution of τ(T)ij at various filter scales shows that all scales are more isotropic than the prediction of rapid distortion theory, with increasing isotropy as scales decrease. A priori tests show that rapid straining does not affect the high correlation and low square-error exhibited by the similarity model...
Large-scale flow effects, energy transfer, and self-similarity on turbulence
Physical Review E, 2006
The effect of large scales on the statistics and dynamics of turbulent fluctuations is studied using data from high resolution direct numerical simulations. Three different kinds of forcing, and spatial resolutions ranging from 256 3 to 1024 3 , are being used. The study is carried out by investigating the nonlinear triadic interactions in Fourier space, transfer functions, structure functions, and probability density functions. Our results show that the large scale flow plays an important role in the development and the statistical properties of the small scale turbulence. The role of helicity is also investigated. We discuss the link between these findings and intermittency, deviations from universality, and possible origins of the bottleneck effect. Finally, we briefly describe the consequences of our results for the subgrid modeling of turbulent flows.
Grid-Scale and Subgrid-Scale Eddies in Turbulent Flows ∼ a Priori Test
2001
Grid-scale (GS) and subgrid-scale (SGS) eddies in homogeneous isotropic turbulence are identified by a priori test. GS and SGS velocity fields are obtained by filtering the DNS velocity field for different Reλ using three classical filters for LES: Gaussian filter, tophat filter and sharp cutoff filter, and the most important filter width is considered as the length of Kolmogorov microscale in the DNS field with a constant multiplication. Eddies in the GS field, i.e., eddies larger than filter width are considered as grid-scale eddies and others are subgrid-scale eddies. Second invariant Q of the velocity gradient tensor is used for identification of these structures in GS and SGS fields. By visualizing the contour surfaces of second invariant Q, it is shown that GS and SGS fields itself contain lots of distinct tube-like eddies in homogeneous isotropic turbulence, which indicates that the DNS field may contain multi-scale structures in turbulent flow.