One-dimensional turbulence modelling of turbulent wall bounded flows

In the first part of the dissertation, a new structure is proposed for turbulent wall bounded flows based on experimental and theoretical analysis of the mean momentum balance. Available high quality data reveal a dynamically relevant four-layer description that is a considerable departure from the mean profile four-layer description traditionally and nearly universally ascribed to turbulent wall flows. Each of the four-layers is characterized by a predominance of two of the three terms in the governing equations, and thus the mean dynamics of these four-layers are unambiguously defined. The inner normalized physical extent of three of the layers exhibits significant Reynolds number dependence. The scaling properties of these layer thicknesses are determined. Particular significance is attached to the viscous/Reynolds stress gradient balance layer since its thickness defines a required length scale. Multiscale analysis substantiates the four-layer structure in fully developed turbulent channel flow. In particular, the analysis verifies the existence of at least one intermediate layer, with its own characteristic scaling, between the traditional inner and outer layers. Further analysis of Fife et al. has shown that stress gradient balance regions are characterized by an intrinsic hierarchy of "scaling layers" (analogous to the inner and outer domains), filling out the stress gradient balance region except for locations near the wall. The spatial extent of each scaling layer is found asymptotically to be proportional to its distance from the wall.; In the second part of the dissertation, a new modeling approach, termed one-dimensional Turbulence (ODT), is applied to study the turbulent wall flows over a wide range of Reynolds number. ODT explicitly represents the two distinct physical processes in turbulent flows: molecular diffusion and turbulent stirring of different size eddies. The distinctive feature of ODT is the representation of turbulent advection by a postulated stochastic mapping event rather than an evolution equation. With the restriction of the model to a one-dimensional spatial domain, all relevant length and time scales for high Reynolds number flows can be resolved. The interaction of molecular diffusion and turbulent stirring effect for all the scales is explicitly represented. Since Fife et al. have shown that the mean flow equations inherently contains a hierarchical layer structure, the hierarchy based model of ODT would seem to have natural advantages.; One-dimensional turbulence (ODT) has been applied for fully developed turbulent channel flow over a range of 10 ≤ Retau ≤ 10,000 and zero pressure gradient turbulent boundary layer over a range of 10 ≤ Retheta ≤ 20,000. In each case the computed mean velocity profile and skin friction coefficient compare well with the experimental data. The model predicts a logarithmic increase of inner scaled streamwise fluctuation peak value with increasing Reynolds number. The trend obtained from ODT agrees well with the recent experimental correlation.