Journal of Fluid Mechanics

Evolution of three-dimensional coherent structures in a flat-plate boundary layer

Dietmar Rempfer a1 and Hermann F. Fasel a2
a1 Institut für Aerodynamik und Gasdynamik, Universität Stuttgart, 70569 Stuttgart, Germany
a2 Department of Aerospace and Mechanical Engineering, The University of Arizona, Tucson, AZ 85721, USA

Article author query
rempfer d   [Google Scholar] 
fasel hf   [Google Scholar] 


Using a data base generated by a numerical simulation, the three-dimensional coherent structures of a transitional, spatially evolving boundary layer are determined and their spatio-temporal behaviour is investigated in detail. The coherent structures are calculated by the proper orthogonal decomposition method (POD), which leads to an expansion of the flow field variables into Karhunen-Loéve eigenfunctions. It is shown that the dynamical coherent structures of the flat-plate boundary layer can be described by pairs of eigenfunctions that contain complete information on the spatial evolution of the structures. It is further demonstrated that first-order coherent structures determined by POD correspond to structures that are observed in experiments. In the region of the boundary layer where the spike signals of transition occur, higher-order coherent structures also play an essential role. By considering these higher-order structures as well as their dynamical behaviour in time, a compact description of the flow phenomena in the boundary layer can be obtained. The description of the events occurring at the spike stages of the transitional boundary layer shows, from a coherent structures point of view, striking similarities to the bursting event of fully turbulent boundary layers.

(Published Online April 26 2006)
(Received December 15 1992)
(Revised July 20 1993)