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

Abstract

The stretched spiral vortex ͓T. S. Lundgren, "Strained spiral vortex model for turbulent structures," Phys. Fluids 25, 2193 ͑1982͔͒ 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 ͑2008͔͒, 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 convergence of the recirculating flow or streamwise roll ͓F. Waleffe, "Homotopy of exact coherent structures in plane shear flows," Phys. Fluids 15, 1517 ͑2003͔͒ caused by the upward and downward motions associated with the streaks. The vortex tube is formed by axial straining and lowering of pressure in the recirculating region. The spanwise shear layers are entrained by the tube and they form spiral turns. The latter symmetric mode tends to be transformed into the former mode with lapse of time due to the action of the pressure Hessian term. The power law in the inertial subrange energy spectrum is studied. The base steady spectrum fits the equilibrium Kolmogorov Ϫ5/3 spectrum, to which a nonequilibrium component induced by the fluctuation of the dissipation rate is added. This component is extracted using the conditional sampling on , and it is shown that it fits the Ϫ7/3 power in accordance with the statistical theory. The correlation between these spectra and the appearance and diminution of the streaks and the two modes of the spiral vortex is discussed. The temporal variations of the spectrum are divided into two regimes, Phases 1 and 2. Large 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 Ϫ7/3 power component.

Flow organization near shear layers in turbulent wall-bounded flows

“…As a consequence, vortex tubes in wall-bounded turbulence are likely to be a by-product, rather than the prime movers of vortex dynamics. Even though definite statements are hard to make given the 'static' nature of our observations, this scenario is consistent with other recent studies [24,37]. It is also important to point out that the apparent thickness of the shear layers and the cross section of the vortex tubes is typically of the order of 10 wall units, which amounts to about five times the Kolmogorov scale away from the wall [32], comparable with the typical dissipative length scale in isotropic turbulence [38].…”

Modulation of homogeneous shear turbulence laden with finite-size particles

“…[50,60] It is very interesting to know how these interactions are modified by the presence of particles. In addition to the direct interaction of vortical structures with particles, we need to understand the interactions of the modified vortical structures Downloaded by [New York University] at 07:08 20 June 2015 with other vortex structures (including the modified ones).…”

Flow resistance in natural, turbulent channel flows: The need for a fluvial fluid mechanics

“…A template model for this phenomenon is the stretched spiral vortex [Lundgren, 1982] shown in Figure 3. Evidence for the existence of this system of vortex tube, with associated vortex sheets has been found in homogeneous isotropic turbulence [Horiuti and Fujisawa, 2008], shear flows [Horiuti and Ozawa, 2011], and boundary layers [Pirozzoli et al, 2010]. Crucially, however, the relative frequency of different modes of behavior of the stretched spiral vortex differed for these cases, which is highly suggestive of a means to place the above results on velocity-intermittency and modulation of the small scales on a process-based footing: the manner by which vortical structures are coupled to larger scales depends upon the stretched vortex modes present (Figure 3) and their mutual interaction.…”

“…A perturbation expansion about the baseline 25/3 spectrum reveals a 27/3 spectrum due to fluctuations in the dissipation rate and these two spectra may be linked to the topology of the stretched spiral vortices [Horiuti and Ozawa, 2011]. Hence, an alternative modeling framework is to work with a transport equation for the subfilter scale kinetic energy and to incorporate topological effects through their consequences for the spectrum.…”