Influence Of The Shear Parameter On Large- And Small-Scale Statistics In Homogeneous Turbulent Shear Flow

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This dissertation consist of three parts. The first part is a study of the asymptotic behavior of large-scale velocity statistics in an homogeneous turbulent shear flow using direct numerical simulations (DNS) of the incompressible Navier-Stokes equations on a 512(exp 3) grid, and with viscous rapid distortion theory (vRDT). We use a novel pseudo-spectral algorithm that allows us to set the initial value of the shear parameter in the range 3-30 without the shortcomings of previous numerical approaches. We find there is an explicit dependence of the early-time behaviour on the initial value of the shear parameter. Moreover, the long-time asymptotes of large-scale quantities such as the ratio of the turbulent kinetic energy production rate over dissipation rate, the Reynolds stress anisotropic tensor, and the shear parameter itself depend sensitively on the initial value of the shear parameter. In the second part, motivated by the numerical results described above, the sensitivity to the initial value of the shear parameter and Reynolds number is investigated for the first time in a wind tunnel. Using an active grid, the initial value of Reynolds number based on the Taylor microscale is varied over the range 100 less than or equal to R (sub lambda) less than or equal to 250. The shear is generated using screens of different solidities followed by a series of straightening channels (Garg and Warhaft (1998)), allowing us to vary the initial value of the shear parameter over the modest range 6 less than or equal to S* (exp 0) less than or equal to 12. We find that the longtime behavior of the shear parameter depends on its initial value over the non-dimensional time interval 5 less than or equal to St less than or equal to 25, but is less sensitive to the initial value of the Reynolds number. The ratio of the turbulent kinetic energy production over dissipation rate appears to show a similar dependence on the initial value of the shear parameter, but there is more significant scatter in the data. We find that the turbulent kinetic energy grows with downstream distance, in agreement with previous work, and that its growth rate too is a stronger function of the initial shear parameter than the initial Reynolds number. The last part consist of a study of the influence of the shear parameter on velocity-gradient statistics such as the rate-of-strain tensor and vorticity. We find that the tails of the probability distribution function of components of the vorticity vector and the rate-of-strain tensor approach a Gaussian distribution with increasing shear parameter. Results are compared with the predictions of v RDT. We also find that increasing the shear parameter causes the main contribution to enstrophy production to shift from the nonlinear terms to the rapid terms (terms that involve the mean strain and vorticity) due to the alignments of the vorticity and the rate-of-strain field.
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