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VORTICITY, STRAIN AND LARGE SCALE STATISTICS AS A FUNCTION OF THE SHEAR PARAMETER AND REYNOLDS NUMBER IN HOMOGENEOUS TURBULENT SHEAR FLOW

Juan C. Isaza
Sibley School of Mechanical & Aerospace Engineering, Cornell University, Ithaca, NY, 14850, US

Lance R. Collins
Sibley School of Mechanical and Aerospace Engineering, Cornell University, USA

Abstract

The asymptotic behavior of large- and small-scale velocity statistics in an homogeneous turbulent shear flow is examined using direct numerical simulations of the incompressible Navier-Stokes equations on a 5123 grid. We used a novel pseudo-spectral algorithm (Brucker et al. 2007) that allows us to set the initial value of the shear parameter in the range 3−30. We have found that large-scale quantities such as the ratio of kinetic energy production over dissipation, and the nondimensional shear parameter reach a self-similar state that depends sensitively on the initial value of the shear parameter. Additionally, we show that the probability density function (PDF) of the vorticity vector and the rate-of-strain tensor approach a Gaussian distribution with increasing initial shear parameter. On the other hand, the tails of the PDFs of the velocity derivatives become more stretched with increasing Reynolds number at fixed shear parameter. We use Viscous Rapid Distortion Theory to explain some of these trends.