A Theoretical Model of the Coherent Structure of the Turbulent Boundary Layer in Zero Pressure Gradient
A self-generating deterministic coherent structure is shown to arise in calculations on a model of a turbulent boundary layer. The solution commences with the evaluation of the linear damped periodic eigen mode for the vertical pertubation which leads to an initial growth in the vorticity perturbations. These lead to changes in the Reynolds stresses and hence to a distortion of the time dependent mean velocity distribution. Our analysis in this respect is somewhat similar to the Benney-Lin investigation of the non-linear interaction of two symmetric oblique waves in unstable laminar boundary layers. The distorted mean velocity profile leads to a strong growth in the Reynolds shear stress, provided the initial disturbance exceeds a certain amplitude of the order of 10% of the freestream velocity. The numerical results display a spanwise periodic structure with a spacing of the order of 100 wall units and have the form of side by side ejections and sweeps. The maximum distortion in the mean velocity occurs near y+ = 20 over a wide range of Reynolds numbers. It is concluded that the distorting mean velocity profile in the inner region of the boundary layer is grossly unstable and will lead to a catastrophic breakdown of the flow into smaller scales, which therefore represents the high production of turbulent energy and its dissipation. This process is self-generating and occurs randomly throughout the turbulent boundary layer.
KeywordsReynolds Stress Turbulent Boundary Layer Coherent Structure Eddy Viscosity Reynolds Shear Stress
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