Boundary layers in turbulent vertical convection at high Prandtl number

Many environmental flows arise due to natural convection at a vertical surface, from flows in buildings to dissolving ice faces at marine-terminating glaciers. We use three-dimensional direct numerical simulations of a vertical channel with differentially heated walls to investigate such convective, turbulent boundary layers. Through the implementation of a multiple-resolution technique, we are able to perform simulations at a wide range of Prandtl numbers ${Pr}$ . This allows us to distinguish the parameter dependences of the horizontal heat flux and the boundary layer widths in terms of the Rayleigh number $\mbox {{Ra}}$ and Prandtl number ${Pr}$ . For the considered parameter range $1\leq {Pr} \leq 100$ , $10^{6} \leq \mbox {{Ra}} \leq 10^{9}$ , we find the flow to be consistent with a ‘buoyancy-controlled’ regime where the heat flux is independent of the wall separation. For given ${Pr}$ , the heat flux is found to scale linearly with the friction velocity $V_\ast$ . Finally, we discuss the implications of our results for the parameterisation of heat and salt fluxes at vertical ice–ocean interfaces.

The fate of particles in a volumetrically heated convective fluid at high Prandtl number

The dynamics of suspensions plays a crucial role in the evolution of geophysical systems such as lava lakes, magma chambers and magma oceans. During their cooling and solidification, these magmatic bodies involve convective viscous fluids and dispersed solid crystals that can form either a cumulate or a floating lid by sedimentation. We study such systems based on internal heating convection experiments in high Prandtl fluids bearing plastic beads. We aim to determine the conditions required to produce a floating lid or a sedimented deposit. We show that, although the sign of particles buoyancy is the key parameter, it is not sufficient to predict the particles fate. To complement the model we introduce the Shields formalism and couple it with scaling laws describing convection. We propose a generalized Shields number that enables a self-consistent description of the fate of particles in the system, especially the possibility to segregate from the convective bulk. We provide a quantification of the partition of the mass of particles in the different potential reservoirs (bulk suspension, floating lid, settled cumulate) through reconciling the suspension stability framework with the Shields formalism. We illustrate the geophysical implications of the model by revisiting the problem of the stability of flotation crusts on solidifying rocky bodies.

Coherent Particle Structures in High-Prandtl-Number Liquid Bridges

Clustering of small rigid spherical particles into particle accumulation structures (PAS) is studied numerically for a high-Prandtl-number (Pr = 68) thermocapillary liquid bridge. The one-way-coupling approach is used for calculation of the particle motion, modeling PAS as an attractor for a single particle. The attractor is created by dissipative forces acting on the particle near the boundary due to the finite size of the particle. These forces can dramatically deflect the particle trajectory from a fluid pathline and transfer it to certain tubular flow structures, called Kolmogorov–Arnold–Moser (KAM) tori, in which the particle is focused and from which it might not escape anymore. The transfer of particles can take place if a KAM torus, which is a property of the flow without particles, enters the narrow boundary layer on the flow boundaries in which the particle experiences extra forces. Since the PAS obtained in this system depends mainly on the finite particle size, it can be classified as a finite-size coherent structure (FSCS).

Active oxygen transport in tissue by interstitial flow

Oxygen (O2) transport through diffusion from capillary to tissue has long been established by Krogh. However, the interstitial fluid in the interspace between tissue and capillary has a high Prandtl number around 103 and hence its convective mass transport is more efficient than its diffusive transport. The interstitial flow drained by the initial lymphatics contributes to the convective transport of O2 through tissue, which can be modeled as aligned blood capillaries in parallel and the initial lymphatics. It is found that both the O2 concentration distribution and the total O2 flux are sensitive to the flow rate of interstitial fluid. The convection contribution has been evaluated based on the Peclet number, feature flow rate, and convection-diffusion boundary. At the same interstitial flow rate, convection delivers more O2 to type I muscle fibers with a higher concentration of myoglobin than to type IIX muscle fibers. Even with a small external force, tissue with a higher specific hydraulic conductance (permeability) has a larger interstitial flow rate and a higher O2 transport rate than those in healthy tissue. Hence, the overall O2 transport from capillary to tissue includes two components, i.e., active convection transport by interstitial flow due to pressure gradient and passive diffusion transport due to concentration gradient. The active convective O2 transport is crucial for the recovery of damaged tissue where the contribution from passive diffusion transport is constrained by regulation of capillary opening. The convection facilitated O2 transport can be the basis for cell differentiation, morphogenesis, and therapeutic effects of massage and acupuncture.Key pointsInterstitial flow plays a key role in active O2 transport in tissue due to its high Prandtl number v/D~103;O2 transport in tissue is balanced by both active convection and passive diffusion transport.Interstitial flow in form of active convective transport can pump more than hundred times of O2 into tissue than those by passive diffusion transport due to the concentration gradient.Active convection transport can be triggered by external pressure, which is crucial for damage tissue recovery.