The turbulent flow in a slug: a re-examination

The transition to turbulence in pipe flow proceeds through several distinct stages, eventually producing aggressively expanding regions of fluctuations, ‘slugs’, surrounded by laminar flow. By examining mean-velocity profiles, fluctuating-velocity profiles and Reynolds stress profiles, the seminal study of Wygnanski & Champagne (J. Fluid Mech., vol. 59 (2), 1973, 281–335) concluded that the flow inside slugs is ‘identical’ to fully turbulent flow. Although this conclusion is widely accepted, upon closer examination of their analysis, we find that their data cannot be used to substantiate this conclusion. We resolve this conflict via new experiments and simulations wherein we pair slugs and fully turbulent flow at the same value of Reynolds number (Re). We conclude that the flow inside a slug is indeed indistinguishable from a fully turbulent flow but only when the two flows share the same value of Re. Our work highlights the rich Re-dependence of transitional pipe flows

The third-order structure function in two dimensions: The Rashomon effect

We study the third-order longitudinal structure function, S3(r), in two-dimensional turbulence. In three dimensions, there is considerable theoretical, experimental, and numerical consensus regarding the validity of Kolmogorov’s arch-famous “four fifth law” for S3(r). By contrast, in two dimensions, two disparate cascades, changed dissipation anomalies, a large-scale drag, and other factors conspire to create several versions of the S3(r) “law.” This single quantity can vary considerably when viewed from different perspectives, reminiscent of the “Rashomon effect” in anthropology. After reviewing the history and usage of S3(r) in two-dimensional turbulence, we show that S3(r) generically embodies a mixture of energy and enstrophy fluxes. Building on this result, we derive S3(r) laws for freely decaying and forced two-dimensional turbulent flows, where we also account for the effects of a large-scale drag, an inextricable feature of quasi two-dimensional turbulence in experimental and atmospheric flows. We draw attention to the caution needed in interpreting S3(r) in two-dimensional turbulence