A Sublayer Bursting Model for Turbulent Boundary Layers
Modelling of turbulence near a wall requires the accurate representation of the statistics of the fluctuating velocities and pressures with as few empirical parameters as possible Commonly used boundary layer turbulence models such as Prandtl’s mixing-length model, large-eddy simulation models or the k- ε model attempt to do this essentially without taking into account the basic structure of the turbulent fluctuating field Landahl (1975, 1990) suggested that the stress-carrying eddies could be modelled as localized disturbances created by small-scale breakdowns due to a local instability or other strong nonlinearity. He showed (1993) that the arising initial-value problem could be solved analytically through a time sequential procedure, in which the linear shear interaction stage will govern the flow during the early times of the order of 1/U’(y),U(y) being the mean velocity distribution, (treated as approximately parallel), with their long-time asymptotes serving as the initial values for the subsequent viscous and nonlinear stages. Calculations presented in Landahl (1990) demonstrated that initial disturbances due to oblique instability waves without spanwise symmetry gave as a result streaky structures with good qualitative agreement with those observed in the near-wall region of a turbulent boundary layer. Here we present a simple model along such lines showing how Prandtl’s (1925) mixing-length theory comes out from averaging a random distribution of initially localized three-dimensional disturbances.
KeywordsBoundary Layer Turbulence Couette Flow Reynolds Shear Stress Initial Disturbance Streaky Structure
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