A scale-invariant statistical theory of turbulence is described. The modified and invariant form of the equation of motion is then solved at the scale of eddy-dynamics, cluster-dynamics, and molecular-dynamics to reveal the internal structure of turbulent boundary layer over a flat plate. The predicted velocity profile is found to be in good agreement with the large body of experimental data reported in the literature. The results suggest that the classical logarithmic law of the wall should be modified. Also, based on an invariant definition of kinematic viscosity, a scale invariant definition of Reynolds number xx x 1 x Re L w / v 1 ββ β β − β− = λ is presented. In the present study, the implications of the scale invariant model of statistical mechanics to the statistical theory of turbulence are further examined. Also, the problem of turbulent flow over a flat plate will be investigated and it will be shown that the analytical solution of the modified equation of motion closely agree with the large body of experimental data available in the literature. The results suggest that the logarithmic law of the wall should be modified.
|Title of host publication||Proceedings of the 5th IASME / WSEAS International Conference on Fluid Mechanics and Aerodynamics|
|Editors||Siavash H. Sohrab, Haris J. Catrakis, Nikolai Kobasko, Sarka Necasova|
|State||Published - 2007|
|Event||The 5th IASME / WSEAS International Conference on Fluid Mechanics and Aerodynamics - Athens, Greece|
Duration: Aug 1 2007 → …
|Conference||The 5th IASME / WSEAS International Conference on Fluid Mechanics and Aerodynamics|
|Period||8/1/07 → …|