Kiyosi Horiuti

Roles of non-aligned eigenvectors of strain-rate and subgrid-scale stress tensors in turbulence generation

Alignment of the eigenvectors for strain-rate tensors and subgrid-scale (SGS) stress tensors in large-eddy simulation (LES) is studied in homogeneous isotropic turbulence. Non-alignment of these two eigenvectors was shown in Tao, Katz & Meneveau (2002). In the present study, the specific term in the decomposition of the SGS stress tensor, which is primarily responsible for causing this non-alignment, is identified using the nonlinear model. The bimodal behaviour of the alignment configuration reported in Tao et al . (2002) was eliminated by reordering the eigenvalues according to the degree of alignment of the corresponding eigenvectors with the vorticity vector. The preferred relative orientation of the eigenvectors was

A classification method for vortex sheet and tube structures in turbulent flows

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Multimode stretched spiral vortex and nonequilibrium energy spectrum in homogeneous shear flow turbulence

. The alignment trends were conditionally sampled based on the relative dominance of strain and vorticity. The effect of the identified term on the alignment was the largest in the region in which the magnitudes of strain and vorticity were comparable and large (flat sheet). The most probable alignment configuration in the flat-sheet region was different from those in the strain-dominated and vorticity-dominated regions. The relative orientation of the eigenvectors was dependent on the degree of resolution for the flat sheet region yielded on the LES mesh. When the alignment was conditionally sampled on the events with the backward scatter of the SGS energy into the grid scale, the interchange of the alignment of the eigenvectors took place. Relevance of the identified term for the generation of turbulence is investigated. It is shown that the identified term makes no contribution to the production of the total SGS energy, but contributes significantly to the generation of the SGS enstrophy. The identified term causes a time-lag in the evolution of the turbulent energy and enstrophy. It is shown that generation of vorticity is markedly attenuated when the magnitude of the identified term is modified, and the original nonlinear model yielded the results which are in the closest agreement with the direct numerical simulation data.

Nonequilibrium energy spectrum in the subgrid-scale one-equation model in large-eddy simulation

A new classification method for structures in turbulent flow is proposed and applied to the analysis of homogeneous isotropic turbulence. The criteria for the classification of the structures into three groups, namely, the group of structures similar to the core region of the Burgers’ vortex tube in which vorticity is predominant, that of the structures similar to the curved sheet in the circumference of the tube core in which strain is predominant, and that of the flat sheets similar to the Burgers’ vortex layer in which vorticity and strain are comparably large, were considered. This method was developed based on the eigenvalue solutions of the λ2 method [Jeong and Hussain, J. Fluid Mech. 285, 69 (1995)] on the basis of the principal strain eigenvectors, which were reordered according to the degrees of alignment with the vorticity vector. Assessment of the proposed method was carried out in fully developed homogeneous isotropic turbulence and in the process of rolling up of the vortex layer in ABC flow....

Similarity modeling on an expanded mesh applied to rotating turbulence

The stretched spiral vortex [T. S. Lundgren, “Strained spiral vortex model for turbulent structures,” Phys. Fluids 25, 2193 (1982)] is identified in turbulence in homogeneous shear flow and the spectral properties of this flow are studied using direct-numerical simulation data. The effects of mean shear on the genesis, growth, and annihilation processes of the spiral vortex are elucidated, and the role of the spiral vortex in the generation of turbulence is shown. As in homogeneous isotropic turbulence [K. Horiuti and T. Fujisawa, “The multi mode stretched spiral vortex in homogeneous isotropic turbulence,” J. Fluid Mech. 595, 341 (2008)], multimodes of the spiral vortex are extracted. Two symmetric modes of configurations with regard to the vorticity alignment along the vortex tube in the core region and dual vortex sheets spiraling around the tube are often educed. One of the two symmetric modes is created by a conventional rolling-up of a single spanwise shear layer. Another one is created by the conve...

Transformation properties of dynamic subgrid-scale models in a frame of reference undergoing rotation

The subgrid-scale (SGS) modeling in large-eddy simulation (LES) which accounts for the effect of unsteadiness and nonequilibrium state in the SGS is considered. Unsteadiness is incorporated by considering the spectral evolution in the forced homogeneous isotropic turbulence using the transport equation for the SGS energy. As for the unfiltered spectrum, perturbative expansion of the Kovasnay spectral model about the Kolmogorov −5/3 energy spectrum which constitutes a base equilibrium state in the inertial subrange, yields the extra components with −7/3 and −9/3 powers. It is shown that these spectra are actually extracted in the direct numerical simulation (DNS) data and these components govern the unsteady energy transfer. As for the SGS real-space representation of the spectral model, we consider the SGS one-equation model. The perturbation expansion is applied to the one-equation model by setting the base SGS energy as the standard Smagorinsky model, which assumes the equilibrium state in the SGS and i...

Alignment of Eigenvectors for Strain Rate and Subgrid-Scale Stress Tensors

Because of the reduction in the turbulent kinetic energy decay rates rotating turbulence presents a significant challenge for turbulence models developed for nonrotating cases. We show that the modeling difficulties are removed if the generalized similarity methods are implemented on an expanded mesh.

Nonequilibrium state in energy spectra and transfer with implications for topological transitions and SGS modeling

Theoretical consideration is presented for the transformation properties of the subgrid-scale (SGS) models for the SGS stress tensor in a non-inertial frame of reference undergoing rotation. As was previously shown (Speziale, C.G., Geophys. Astrophys. Fluid Dynamics 33, 199 (1985)), an extra correction term is yielded for the SGS stress tensor in the transformation of a rotating frame relative to an inertial framing. We derived the exact expression for the correction term for the spherical Gaussian filter function. Certain transformation rules are imposed on the SGS stress by the derived correction term, namely the SGS stress is not indifferent to a frame rotation, but the divergence of the SGS stress is frame indifferent. Conformity of the modelled SGS stress tensor estimated using the previous dynamic SGS models (the dynamic Smagorinsky, dynamic mixed and nonlinear models) with these transformation rules is examined. It is shown that values for certain model parameters contained in the mixed models can be theoretically determined by imposing these rules. We have conducted the a priori and a postepriori numerical assessments of the SGS models in decaying homogeneous turbulence which is subjected to rotation. All of the previous dynamic models were found to violate the rules except for the nonlinear model. The nonlinear model is form invariant, but the result obtained using the nonlinear model showed significant deviation from the DNS data. Failure of previous models was attributable to insufficient accuracy in approximating the modified cross term in the decomposition of the SGS stress tensor. A dynamic mixed model is proposed to eliminate the truncation error for the modelled correction term, in which multilevel filtering of the velocity field was utilized. The proposed model obeyed the transformation rules when the level of the multifiltering operation was large. It was shown that the defiltered model is derived in the limit of the infinite level of multifiltering and that the defiltered model is form invariant.

Assessment of the Generalized Normal Stress and the Bardina Reynolds Stress Subgrid-Scale Models in Large Eddy Simulation

Alignment of the eigenvectors for strain rate tensor and subgrid-scale (SGS) stress tensor is studied using the direct numerical simulation data for incompressible homogeneous isotropic turbulence. Non-alignment of these two eigenvectors was previously reported in Tao, Katz and Meneveau (2000). In the present study, the term which is primarily responsible for causing this non-alignment is identified in the decomposition of the SGS stress tensor obtained using the nonlinear model. It is shown that the eigenvectors for the SGS stress tensor have a strongly preferred relative orientation of 45 degrees with the strain rate eigenvectors. This angle of 45 degrees is slightly larger than that reported in Tao et al. (2000) (34 degrees), but the present result was consistent with the angles calculated using the Burgers’ vortex tube and layer models. When the identified term was subtracted from the SGS stress tensor, the strain eigenvector was placed almost parallel to the stress eigenvector. Relevance of this identified term for generation of energy cascade and vortex stretching is investigated. It is shown that this term makes no significant contribution to the SGS production term, whereas it significantly contributes to the generation of vorticity associated with the backward scatter of the SGS energy into grid-scale.

Coherent Structure and Subgrid-Scale Energy Transfer in Turbulence

This paper reviews the recent progress in studies on the nonequilibrium statistics of turbulence. The structure of the energy spectrum in the inertial subrange is studied using direct numerical simulation (DNS) data for turbulence in a periodic box at high Reynolds numbers. A perturbation expansion for the energy spectrum about a base Kolmogorov k(-5/3) steady state yields additional -7/3 and -9/3 power components that are induced by the fluctuation of the dissipation rate epsilon and represents a nonequilibrium state. The nonequilibrium component is extracted by applying a conditional sampling on d epsilon/dt to the DNS data, and it is shown that the deviation from the base -5/3 spectrum fits the -7/3and -9/3 power slopes. The temporal development of the spectrum is divided into two regimes, phases 1 and 2. The large amount of energy contained in the low-wavenumber range in Phase 1 is cascaded to the small scales in Phase 2. This energy transfer is accomplished by the reversal in the sign of the -7/3 power component. Correlation of the appearance of the nonequilibrium spectrum and the transition in the mode of the configuration of the stretched spiral vortex is discussed. Occurrence of transition is identified using the helicity. Subgrid-scale (SGS) modeling in LES that accounts for the effect of unsteadiness and nonequilibrium state is considered by employing the transport equation for the SGS energy (one-equation model). Perturbation expansion about the Kolmogorov -5/3 energy spectrum which constitutes a base equilibrium state in the inertial subrange yields -7/3 spectrum as in the unfiltered case. These spectra are extracted in the DNS data, and their roles in the generation of the energy cascade are revealed. The SGS energy spectrum which governs the one-equation model is sought in a perturbative manner. Besides the base -5/3 spectrum assumed in the Smagorinsky model, -7/3 power component is derived, which is induced by temporal variations of SGS energy. The nonequilibrium Smagorinsky model in which estimate of the SGS energy based on the -7/3 spectrum is added to the Smagorinsky model is proposed. Assessment of the nonequilibrium Smagorinsky model in forced homogeneous isotropic turbulence showed that the performance of the Smagorinsky and one-equation models for prediction of temporal variations of turbulence energy is not satisfactory, but improvement is achieved in the new model.