On the relation between kinetic energy production in adverse-pressure gradient wall turbulence and streak instability

Abstract

A direct numerical simulation (DNS) of a turbulent channel flow with a lower curved wall is performed at Reynolds number Re _τ≃617 at inlet. This adverse-pressure gradient turbulent flow is characterized by strong peaks of turbulent kinetic energy at both walls, as a consequence of the breakdown of more organized flow structures. To elucidate the underlying instability scenario, low-speed streak structures are extracted from the turbulent flow field and base flows formed with conditional streak averages, superimposing the mean streamwise velocity profile, are used for linear stability analyses. The size and shape of the counter-rotating streamwise vortices associated with the instability modes are shown to be reminiscent of the coherent vortices emerging from the streak skeletons in the direct numerical simulation. The distance of the streak's centre from the wall is used as a criterion for the conditional averages and the corresponding streak base flows are characterised by more or less pronounced contours of inflection points in the averaging windows normal to the wall. It is shown that the strength of instability of the streak base flows can be inferred from a simplified 1D stability analysis, using local inflectional profiles at different spanwise locations.

Keywords:

• instability
• turbulent boundary layers
• adverse pressure gradient
• direct numerical simulation

Acknowledgment

This work was supported by WALLTURB (a European synergy for the assessment of wall turbulence) which is funded by the EC under the 6th framework program (CONTRACT: AST4-CT-2005-516008) and CISIT (International Campus on Safety and Inter-modality in Transport). The DNS was performed through two successive DEISA Extreme Computing Initiatives (DEISA is a Distributed European Infrastructure for Supercomputing Applications). This work was granted access to the HPC resources of IDRIS under the allocation 2011-021741 made by GENCI (Grand Equipement National de Calcul Intensif).