Our understanding of the material organization of complex fluid flows has benefited recently from mathematical developments in the theory of objective coherent structures. These methods have provided a wealth of approaches that identify transport barriers in three-dimensional (3-D) turbulent flows. Specifically, theoretical advances have been incorporated into numerical algorithms that extract the most influential advective, diffusive and active barriers to transport from data sets in a frame-indifferent fashion. To date, however, there has been very limited investigation into these objectively defined transport barriers in 3-D unsteady flows with complicated spatiotemporal dynamics. Similarly, no systematic comparison of advective, diffusive and active barriers has been carried out in a 3-D flow with both thermally driven and mechanically modified structures. In our study, we utilize simulations of turbulent rotating Rayleigh–Bénard convection to uncover the interplay between advective transport barriers (Lagrangian coherent structures), material barriers to diffusive heat transport, and objective Eulerian barriers to momentum transport. For a range of (inverse) Rossby numbers, we identify each type of barrier and find intriguing relationships between momentum and heat transport that can be related to changes in the relative influence of mechanical and thermal forces. Further connections between bulk behaviours and structure-specific behaviours are also developed.

Polymers in a turbulent flow are stretched out by the fluctuating velocity gradient and exhibit a broad distribution of extensions $R$; the stationary probability density function (p.d.f.) of $R$ has a power-law tail with an exponent that increases with the Weissenberg number $\mathit {Wi}$, a non-dimensional measure of polymer elasticity. This study addresses the following questions. (i) What is the role of the non-Gaussian statistics of the turbulent velocity gradient on polymer stretching? (ii) How does the p.d.f. of $R$ evolve to its asymptotic stationary form? Our analysis is based on simulations of the dynamics of finitely extensible bead–spring dumbbells and chains, in the extremely dilute limit, that are transported in a homogeneous and isotropic turbulent flow, as well as in a Gaussian random flow. We show that while the turbulent flow is more effective at stretching small-$\mathit {Wi}$ stiff polymers, the Gaussian flow is more effective for high-$\mathit {Wi}$ polymers. This suggests that high-$\mathit {Wi}$ polymers (with large relaxation times) are stretched primarily by the cumulative effect of moderate strain rate events, rather than by short-lived extreme-valued strain rates. Next, we show that, beginning from a distribution of coiled polymers, the p.d.f. of $R$ exhibits two distinct regimes of evolution. At low to moderate $\mathit {Wi}$, the p.d.f. quickly develops a power-law tail with an exponent that evolves in time and approaches its stationary value exponentially. At high $\mathit {Wi}$, the rapid stretching of polymers first produces a peak in the p.d.f. near their maximum extension; a power law with a constant exponent then emerges and expands its range towards smaller $R$. The time scales of equilibration, measured as a function of $\mathit {Wi}$, point to a critical slowing down at the coil–stretch transition. Importantly, these results show no qualitative change when chains in a turbulent flow are replaced by dumbbells in a Gaussian flow, thereby supporting the use of the latter for reduced-order modelling.

Langmuir circulations (LCs) arise through the interaction between the Lagrangian drift of the surface waves and the wind-driven shear layer. Quasi-streamwise vortices (QSVs) also form in the turbulent shear layer next to a flat surface. Both vortical structures manifest themselves by inducing wind-aligned streaks on the surface. In this study, numerical simulations of a stress-driven turbulent shear layer bounded by monochromatic surface waves are conducted to reveal the vortical structures of LCs and QSVs, and their interactions. The LC structure is educed from conditional averaging guided by the signatures of predominant streaks obtained from empirical mode decomposition; the width of the averaged LC pair is found to be comparable to the most unstable wavelength of the Craik–Leibovich equation. Coherent vortical structures (CVSs) are identified using a detection criterion based on local analysis of the velocity-gradient tensor and their topological geometry; QSVs accumulated beneath the windward surface are found to dominate the distribution. Employing the variable-interval spatial average to the identified QSVs further reveals that QSVs tend to form in the edge vicinity of the surface streaks induced by the LCs. The transport budgets of streamwise enstrophy are examined to reveal the interaction. It is found that QSVs perturb the streaks resulting in a localized streamwise gradient of the spanwise velocity, that is, vertical vorticity. The vertical shear tilts the vertical vorticity, therefore enhancing streamwise enstrophy production and the formation of QSVs. The results highlight the differences in the CVSs between the Langmuir turbulence and the wall turbulence.