Streak instability in near-wall turbulence revisited

ABSTRACT

The regeneration cycle of streaks and streamwise vortices plays a central role in the sustainment of near-wall turbulence. In particular, the streak breakdown phase in the regeneration cycle is the core process in the formation of the streamwise vortices, but its current understanding is limited particularly in a real turbulent environment. This study is aimed at gaining fundamental insight into the underlying physical mechanism of the streak breakdown in the presence of background turbulent fluctuation. We perform a numerical experiment based on direct numerical simulation, in which streaks are artificially generated by a body forcing computed from previous linear theory. Upon increasing the forcing amplitude, the artificially driven streaks are found to generate an intense fluctuation of the wall-normal and spanwise velocities in a fairly large range of amplitudes. This cross-streamwise velocity fluctuation shows its maximum at λ⁺ _x ≈ 200 − 300 (λ⁺ _x is the inner-scaled streamwise wavelength), but it only appears for λ⁺ _x ≲ 3000 − 4000. Further examination with dynamic mode decomposition reveals that the related flow field is composed of sinuous meandering motion of the driven streaks and alternating cross-streamwise velocity structures, clearly reminiscent of sinuous-mode streak instability found in previous studies. Finally, it is shown that these structures are reasonably well aligned along the critical layer of the secondary instability, indicating that the surrounding turbulence does not significantly modify the inviscid inflectional mechanism of the streak breakdown via streak instability and/or streak transient growth.

KEYWORDS:

• Streak instability
• sinuous mode
• streamwise vortices
• regeneration mechanism

Acknowledgements

This paper is dedicated to the celebration of 70th birthday of Prof. Javier Jiménez. Especially, the last author of this paper (Yongyun Hwang) has been privileged with productive scientific communication with Javier over a number of years, and gratefully acknowledges this. This work is supported by Engineering and Physical Sciences Research Council (EPSRC) in the UK (EP/N019342/1).

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Engineering and Physical Sciences Research Council [grant number EP/N019342/1].