Spatial Optimal Disturbances in Turbulent Boundary Layers

In this dissertation, disturbances leading to optimal energy growth in a spatially developing, zero-pressure-gradient turbulent boundary layer are examined. The slow development of the turbulent mean flow in the streamwise direction is modeled through a parabolized formulation to enable a spatial marching procedure. In the present framework, the linearized equations subject to a turbulent forcing are solved at particular wavenumber combinations. Conventional spatial optimal disturbance then arise naturally as the homogeneous solution whereas the particular solution captures the response to distributed forcing. A wave-like decomposition for the disturbance is considered to incorporate both conventional stationary modes as well as propagating modes formed by nonzero frequency/streamwise wavenumber and representative of convective structures naturally observed in wall turbulence. The optimal streamwise wavenumber, which varies with the spatial development of the turbulent mean flow, is computed locally via an auxiliary optimization constraint. The present approach can then be considered, in part, as an extension of the resolvent-based analyses for slowly developing flows. Optimization results reveal highly amplified disturbances for both stationary and propagating modes. In all cases, propagating modes surpass their stationary counterpart in both energy amplification and relative contribution to total fluctuation energy. We identify three classes of energetic modes associated with the inner, logarithmic and wake layers of the turbulent mean flow. The inner scaled modes are associated with the ubiquitous near wall streaks residing in the buffer layer. The outer scaled wake modes agree well with the large-scale motions that populate the wake layer. For high Reynolds numbers, however, the log modes increasingly dominate the energy spectra with the predicted streamwise and wall-normal scales in agreement with superstructures observed in turbulent boundary layers. Preliminary experimental measurements are performed to relate the energetic spanwise modes to the reported optimal disturbances.