Linear transient growth in transitional turbulent channel flow at low Reynolds number (Applied mathematical and physical aspects of inhomogeneous turbulence)

Abstract

Generation process of a large stripy pattern of localized turbulence in pressure-driven plane channel flow under a subcritical transitional regime is considered. The most amplified kinetic energy of linear Navier-Stokes equations was computed for each mode in terms of the streamwise and spanwise wavelengths, with applying an eddy viscosity as the nonliner effect. In the study, we focused on the generation state of a turbulence spot, where the localized turbulence would grow or remain in a form of oblique band, or the turbulent stripe. With considering the large-scale secondary flow around the spot or along the oblique band as a base flow, we found specific pairs of wavelengths that are more amplified by the existence of spanwise velocity component in the base flow. It implies that the spanwise flow around a turbulence spot makes flow unstable in the oblique direction, to cause a stripy pattern of turbulence region.