Triple decomposition of velocity gradient tensor in homogeneous isotropic turbulence

Abstract

The triple decomposition of a velocity gradient tensor is studied with direct numerical simulations of homogeneous isotropic turbulence, where the velocity gradient tensor ∇u is decomposed into three components representing an irrotational straining motion (∇u) EL , a rigid-body rotation (∇u) RR , and a shearing motion (∇u) SH . Strength of these motions can be quantified with the decomposed components. A procedure of the triple decomposition is proposed for three-dimensional flows, where the decomposition is applied in a basic reference frame identified by examining a finite number of reference frames obtained by three sequential rotational transformations of a Cartesian coordinate. Even though more than one basic reference frame may be available for the triple decomposition, the results of the decomposition depend little on the choice of basic reference frame. In homogeneous isotropic turbulence, regions with strong rigid-body rotations or straining motions are highly intermittent in space, while most flow regions exhibit moderately ✩ Accepted for publication. https://doi.

Characteristics of small-scale shear layers in a temporally evolving turbulent planar jet

“…These distributions of , and in the planar jet are consistent with DNS results of homogeneous isotropic turbulence (Nagata et al. 2020).

Figure 7.Colour contour plots of ( a ) , ( b ) and ( c ) on an – plane in the planar jet with ().

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“…2015; Nagata et al. 2020). The shear layers in the planar jet are investigated with the method proposed in Watanabe et al.…”

“…In our previous study, a numerical algorithm of the triple decomposition for the full velocity gradient tensor with and was developed and tested with direct numerical simulation (DNS) databases of homogeneous isotropic turbulence (Nagata et al. 2020). This method was used to investigate the shear layers in homogeneous isotropic turbulence in Watanabe et al.…”

Revisiting turbulence small-scale behavior using velocity gradient triple decomposition

“…This decomposition has led to important insight into small-scale intermittency [1][2][3], intense structures in turbulence [4][5][6][7] and local streamline geometry [8][9][10]. However, recent studies [11][12][13] have shown that strain-rate and vorticity do not clearly identify the presence of normal-straining and rigid-body-rotation of the fluid. The presence of shear in both strain-rate and vorticity often obscures our understanding of some of the fundamental phenomena in turbulence.…”

“…This technique has been used for vortex-structure identification and investigation of internal shear layers in wall-bounded flows [14][15][16]. It has recently been used for investigating regions of strong shearing or rotation and detecting internal shear layer in homogeneous isotropic turbulence at Taylor Reynolds numbers, Re λ = 27 and 140 [13]. Aside from Kolář's method, Gao and Liu [12] formulated a "Rortex"-based VGT decomposition for locally fluid-rotational points (VGT has complex eigenvalues) in a turbulent flow field.…”