Interplay between advective, diffusive and active barriers in (rotating) Rayleigh–Bénard flow

Abstract

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.

Variational construction of tubular and toroidal streamsurfaces for flow visualization

“…It is also important to note that [15] defines transport barriers as material structures, which need to satisfy the requirement of objectivity (also known as frame-indifference) [30]. The objective structures extracted from the barrier-equation have also been compared with other Lagrangian and Eulerian coherent structures in [16,31]. For a recent review, we refer to [32].…”

Approaching coherent turbulence and the roll-cell transition with Lagrangian coherent structures and objective fluxes

“…The above research all relied on two-dimensional projections of velocity fields to describe inherently three-dimensional phenomena. Only recently have studies of elliptic LCS and objective momentum and heat transport barriers been successfully conducted in fully threedimensional turbulent experimental and numerical flows (Neamtu-Halic et al 2019;Aksamit and Haller 2022;Aksamit et al 2023).…”

“…We can extend this analysis to three-dimensional flows where locations of elliptic LCSs can be identified as smooth cylindrical LAVD level-surfaces that surround a onedimensional LAVD ridge (Neamtu-Halic et al 2019). In the present work we rely on the relaxed coherent Lagrangian vortex criteria utilized by Aksamit et al (2023) in rotating Rayleigh-Bénard convection by not seeking a central LAVD ridge or enforcing a cylindrical shape. Neglecting these requirements comes with a computational advantage, while still capturing material rotational features.…”

“…Neglecting these requirements comes with a computational advantage, while still capturing material rotational features. In fact, Aksamit et al (2023) showed that any arbitrary LAVD level-surface exhibits exceptional momentum and heat transport blocking behaviour orthogonal to its surface, even though the calculation of LAVD does not consider these fields. Furthermore, the ability of arbitrary LAVD surfaces to organize the transport of momentum and heat was largely independent of the length of the integration time [𝑡 0 , 𝑡 1 ],…”

“…The integrands of equations ( 1) and ( 2) thus provide objective vector fields for quantifying the magnitude and alignment of diffusive heat and momentum transport for arbitrary surfaces in a flow. This frame-indifferent and individual feature-focused approach to quantifying heat and momentum flux has helped explain the relative influences of Coriolis and convective forces on specific vortices in direct numerical simulations of rotating Rayleigh-Bénard flow (Aksamit et al 2023). We apply a similar approach to suggest a spatially and temporally resolved objective diagnostic that predicts the dominance of rolls and cells and is based on the underlying physics of heat and momentum transport.…”