Flat-Eddy Model for Coherent Structures in Boundary Layer Turbulence
An inviscid model for a “flat” eddy, i.e., a localized flow structure with large horizontal dimensions compared to its vertical extent (Landahl 1978, 1983, 1984; Russell and Landahl 1984), is explored further for the study of coherent structures in the wall region of a turbulent boundary layer or channel flow. Flat eddies may be excited by mixing in local instability regions, as may form, for example, in the thin internal shear layers produced by stretching of spanwise vorticity. Conditional sampling of the equations of motion establishes the relation beween the noncoherent motion due to local instability and the coherent structure. By making some reasonable assumptions about the statistical properties of the turbulent stresses produced by a region of local instability a model for a “typical” eddy is constructed. Comparisons with a linearized version of this model with VITA-educed sampled velocity signatures from measurements in a channel flow show good qualitative and quantitative agreement between theory and experiments for the later periods during the bursting cycle. The nonlinear version of the model applied to eddies that are highly elongated in the streamwise direction shows many of the qualitative features seen in experiments such as shear layer formation and the possible appearance of strong, localized ejection.
KeywordsShear Layer Coherent Structure Turbulent Stress Fluid Element Local Instability
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