Physics – Fluid Dynamics
Scientific paper
2009-10-12
Physics
Fluid Dynamics
218 pages, 78 figures
Scientific paper
In this visualisation the instantaneous local velocity is expressed in terms of four components to capture the development of and interactions between coherent structures in turbulent flows. It is then possible to isolate the terms linked with each major type of structure and identify the corresponding subsets of the Navier-Stokes equations that are easier to solve than the full version. Each of these subsets applies to a domain in the flow field not a flow regime. The traditional statistics of turbulence are shown to be not specific to turbulent flow. In particular the Reynolds stresses, the probability density function, the dissipation, the production and the energy spectrum are obtained from one subset associated with unsteady "laminar" flow. The evidence also indicates that the Kolmogorov scale does not represent an eddy size and more importantly that it does not require the assumption of local isotropy. Applications of this visualisation include a proposal for a theoretical closure of the Reynolds equations, the collapse of velocity and skin friction profiles for Newtonian and non-Newtonian fluid flows in all geometries into unique master curves. A new partial derivative is introduced that decouples the effect of diffusion and convection simplifying the mathematical solution of subsets of the NS equations with implications for a more efficient generation of computational fluid dynamics packages. Finally the consequences to turbulent heat and mass transfer are examined.
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