Statistical properties of shear and non-shear velocity components in isotropic turbulence and turbulent jets
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This article may be found at https://doi.org/10.1103/PhysRevFluids.8.104602.
Abstract
The triple decomposition of a velocity gradient tensor, which extracts local fluid motions of shear, rigid-body rotation, and irrotational strain, is extended to the decomposition of velocity vectors into shear and nonshear components. The present approach adapts the Biot-Savart law to reconstruct shear and nonshear velocities from the vorticity vectors of shear and rigid-body rotation, respectively. These velocities are related to the flows induced by small-scale shear layers or vortex tubes. The decomposed velocities are investigated with direct numerical simulations of isotropic turbulence and temporally evolving planar jets. The r.m.s. values of shear and nonshear velocities are about 70% and 30% of the r.m.s. value of total velocity fluctuations, and shear layers have a greater contribution to velocity fluctuations than vortex tubes. The shear and nonshear velocities are positively correlated at large scales, and the momentum transfer due to their interaction actively occurs at scales greater than 20 times the Kolmogorov scale. The contributions of shear and nonshear velocities to the Reynolds stress hardly depend on flows. The energy spectra of these velocities collapse well at small scales under Kolmogorov normalization. The present analysis of the turbulent jet confirms that shearing motion has dominant contributions to the production and diffusion of turbulent kinetic energy and the turbulent transport of a passive scalar. In addition, the energy transfer across scales is shown to be dominated by the large-scale velocity gradients arising from shearing motion and the small-scale stresses due to the shear velocity and its interaction with the nonshear component.
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