DNS study on the regularity of turbulent spot formation in plane channel flow

  • Ono, Ryoko (Department of Mechanical and Aerospace Engine)
  • Matsukawa, Yuki (Department of Mechanical and Aerospace Engine)
  • Kohyama, Kazuki (Department of Mechanical and Aerospace Engine)
  • Tsukahara, Takahiro (Department of Mechanical and Aerospace Engine)

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Reverse transition in channel flow is a phenomenon widely encountered in applications such as heat exchangers and chemical processing, and understanding its fundamental mechanisms is therefore of practical importance. In particular, during subcritical transition, turbulence becomes spatially localized and forms quasi-regular stripe or band patterns, which affect the global criticality and heat/mass transfer performance. Previous studies on such pattern formation have mostly focused either on quasi-static reductions of the Reynolds number or on the evolution toward equilibrium following the application of uniform or localized strong disturbances to a laminar base flow. Substantial progress has been made in characterizing the properties of turbulent stripe and bands in statistically steady states. However, the responsiveness of pattern formation to time-dependent variations in the Reynolds number remains unexplored. Our preliminary DNSs (direct numerical simulations) have revealed that, for a certain rates of the temporal decrease in the friction Reynolds number, turbulence survives in a spot-like localized form and subsequently grows into oblique bands. To examine this transient phase from a spatially uniform turbulent state to spot-like localization, we perform DNS in a computational domain whose streamwise and spanwise lengths are 4096 and 512 times the channel half-gap, respectively. Near the moment when the turbulent kinetic energy attains its minimum value after the friction Reynolds number reduction, the wall-normal velocity fluctuation is employed for visualization because it allows a clear distinction between turbulent and non-turbulent regions. Using a two-point spatial correlation for a local turbulence indicator, we observe non-negligible correlations extending over distances exceeding 100 times the channel half-gap. This result indicates the presence of nontrivial spatial regularity in the formation of turbulent spots, even before the emergence of stripe- or band-like patterns.