On the origin of streamwise vortices in a turbulent boundary layer

Abstract : Several experiments have suggested that the streamwise vortices, with their accompanying low momentum streaks, in a turbulent boundary layer have a characteristic spanwise wavelength of approximately lambda (superscript + subscript z) = 100. A mechanism is proposed which selects a comparable spanwise wavelength and produces counterrotating streamwise vortices in a turbulent boundary layer. Examining the equations which describe the small deviation of the velocity field from its time-average, it is found that the Benney-Gustavsson resonance (Studies in Applied Mathematics 3, 1981) occurs with such a boundary layer velocity profile. It is shown that, as an integral part of this resonance, there is a mean secondary flow which has a spanwise wavelength lambda (superscript +, subscript z) = 90 and whose velocities exhibit a counter-rotating streamwise vortex structure. Keywords include: Turbulent boundary layer; Streamwise vortices; Low-speed streaks; Tollmien-Schlichting waves; vertical vorticity; Resonant interaction; and Weakly non-linear induced flow.