Structure of Turbulence


Experimental results are presented that reveal the structure of a two-dimensional turbulent boundary layer which has been investigated by measuring the time-dependent vorticity flux at the wall, vorticity vector, strain-rate tensor and dissipation-rate tensor in the near wall region with spatial resolution of the order of seven Kolmogorov viscous length scales. Considerations of the structure function of velocity and pressure, which constitute vorticity flux and vorticity, indicated that, in the limit of vanishing distance, the maximum attainable content of these quantities which corresponds to unrestricted resolution, is determined by Taylor's microscale. It also indicated that most of the contributions to vorticity or vorticity flux come from the uncorrelated part of the two signals involved. The measurements allowed the computation of all components of the vorticity stretching vector, which indicates the rate of change of vorticity on a Lagrangian reference frame, and several matrix invariants of the velocity gradient or strain-rate tensor and terms appearing in the transport equations of vorticity, strain-rate and their squared fluctuations. The orientation of vorticity revealed several preferential directions. During bursts or sweeps vorticity is inclined 45o to the longitudinal direction. The results of the joint probability distributions of the vorticity vector orientation angles showed that these angles maybe related to those of hairpin vortex structures. It was also found that there is high probability of the vorticity vector to align with the direction of the intermediate extensive strain corresponding to the middle eigen vector of the strain-rate matrix. All invariants considered exhibit a very strong intermittent behavior which is characterized by large amplitude bursts which may be of the order of 10 r.m.s. value. Small scale motions dominated by high rates of turbulent kinetic energy dissipation and high enstrophy density are of particular interest. It appears that the fluctuating strain field dominates the fluctuations of pressure more than enstrophy. On many instances, local high values of the invariants are also associated with peaks in the shear stress.

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