Reynolds number effect on the Lagrangian evolution of hairpin vortices in turbulent channel flow

Abstract

The evolution and generation of hairpins are studied in a Lagrangian perspective in turbulent channel flows. Direct numerical simulation database of turbulent channel flow at friction Reynolds numbers $R{e}_{\tau }=$590, 390, and 180 is employed to perform tracking and interpolation algorithms of fluid particles on hairpins. These particles are carefully selected using a vortex line identification technique developed to extract the hairpin's core line. Interesting results are observed regarding the Reynolds number impact on the evolution and regeneration of hairpins. As the Reynolds number increases, the head and the vortical tongues are compressed and aligned in the main flow direction and the hairpin structures tend to orient more horizontally. The deformation shape of hairpins using the strain state parameter, which is correlated with the dissipation rate, is analysed using the probability density function. Most phenomena related to the generation of secondary hairpins, including the existence of vortical tongues, occur in the range $35\lesssim y^{+}\lesssim 50$. The results reveal that the Lagrangian perspective is a proper technique to address the extension of vortical tongues, generation of the secondary hairpin, and stretch of hairpin legs.

Keywords:

• Reynolds number effect
• Lagrangian evolution
• hairpin deformation
• fluid particle tracking
• turbulent channel flow

Acknowledgments

BK and ZP would like to acknowledge Dr. Amin Rasam for his fruitful comments and contribution to this work.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 The 4th order Runge-Kutta