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.

Arterial vasodilation drives convective fluid flow in the brain: a poroelastic model

The movement of fluid into, through, and out of the brain plays an important role in clearing metabolic waste. However, there is controversy regarding the mechanisms driving fluid movement, and whether the movement metabolic waste is primarily driven by diffusion or convection. The dilation of penetrating arterioles in the brain in response to increases in neural activity (neurovascular coupling) is an attractive candidate for driving fluid circulation, as it drives deformation of the brain tissue and of the paravascular space around arteries, resulting in fluid movement. We simulated the effects of vasodilation on fluid movement into and out of the brain using a novel poroelastic model of brain tissue. We found that arteriolar dilations could drive convective flow through the brain radially outward from the arteriole, and that this flow is sensitive to the dynamics of the dilation. Simulations of sleep-like conditions, with larger vasodilations and increased extracellular volume in the brain showed enhanced movement of fluid from the paravascular space into the brain. Our simulations suggest that both sensory-evoked and sleep-related arteriolar dilations can drive convective flow of cerebrospinal fluid from the paravascular space into the brain tissue around arterioles.

Convective instability of air flows in the exhaust shaft above a four-row finned beam

Herein, multidirectional quasiperiodic air flows in an exhaust shaft above a four-order horizontal bundle consisting of bimetallic finned tubes used to remove heat in heat exchangers are considered. Modeling of the air movement is carried out on the basis of equations for thermogravitational convection in the Boussinesq approximation. It takes into account the viscosity of the air and the dependence of the air density on the temperature. An interpretation of quasiperiodic airstreams is proposed on the basis of Rayleigh – Bénard convection, as a result of which regular structures, called Rayleigh – Bénard cells, are formed in a liquid or gas. Rayleigh – Bénard cells are an analytical solution to the problem of the stability of hydrodynamics flows in the linear approximation. The appearance of two-dimensional (convective rolls) and threedimensional (rectangular cells) is possible. To estimate the number of emerging structures, the critical Rayleigh numbers were calculated, which characterizes the transition from an unstable mode of the convective fluid flow to a stable mode. For two experiments, the experimental Rayleigh numbers are compared with their critical values. The differences between the experimental conditions and the ideal boundary conditions used in the calculations and the partial destruction of quasiperiodic structures as a result of this are also discussed.

An Efficient Numerical Simulation of 2D Natural Convection in an Inclined Cavity with Internal Heat Generation Using Differential Quadrature Method

Natural laminar convective fluid flow has been simulated inside inclined rectangular cavities with and without internal heat generation for different aspect ratios and inclination angles. The most important basic dimensionless parameters for this problem are the external Rayleigh number (RaE) and the internal Rayleigh number (RaI), where RaE refers to the effects of the differential heating of the side walls and RaI refers to the amount of heat produced internally. Results were obtained for 4 cases with 192 tests: case (1), RaI = 0 without internal source generation, and cases (2, 3, and 4) with internal source generation for RaI = RaE, 10 RaE, and 100 RaE, respectively. In all cases, the parameters of study changed as 103 ≤ RaE ≤106, 0 ≤ RaI ≤ 107, inclination angle from 0 to 60 deg., and aspect ratios of the enclosure from 0.5 to 2. Results were represented graphically for flow and thermal fields as a streamline, isothermal contours, and Nusselt number. The computed results show that the strength of convection currents is measured by the internal energy. Finally, it is illustrated that by using a few grid points and a shorter CPU time for calculation, the present method can produce accurate numerical results. Also, increase in RaI leads to increasing heat transfer rate and its direction out from the cavity at both hot and cold walls. For lower values of RaI, heat transfer diffusion is more prominent, while for higher values of RaI, convection outweighs diffusion. HIGHLIGHTS Natural laminar convective fluid flow inside inclined rectangular cavities with and without internal heat generation for different aspect ratios and inclination angles has been simulated The most important basic dimensionless parameters, the external Rayleigh number (RaE) and the internal Rayleigh number (RaI) are studied DQ method performance was excellent The obtained computational results indicate that the strength of the convection currents depends on the internal energy Accurate numerical results can be obtained by the present method using a few grid points and shorter CPU time for calculation GRAPHICAL ABSTRACT

Possible approach to detecting the mysterious Saturnian convective dynamo through gravitational sounding

Context. Planetary dynamo research is mathematically and numerically difficult. Forward calculations are numerically expensive and subject to much uncertainty in key magnetohydrodynamics parameters. For a gaseous planet such as Saturn, even the precise location of its dynamo and typical convective strength are unknown, which further complicates studies. Aims. We test the idea of inversely probing Saturnian convective dynamo through gravitational sounding, based on the principle that the convective fluid motion can distort the internal density distribution and hence induce the gravitational anomaly. Methods. The Cassini Grand Finale mission has reported unprecedentedly accurate measurements of the gravitational field of Saturn. An unexplained nonaxisymmetric component of the gravitational field was detected in the data. By performing precise orbit determination (POD) simulations, we studied the possibility that the Cassini spacecraft might sense the dynamo-related nonaxisymmetric gravitational signature in the Grand Finale phase. In addition, further extensively simulated missions of various orbit configurations were carried out in order to explore promising mission strategies that might fulfill the objective of detecting the Saturnian convective dynamo. Results. Our POD simulations show that the gravity science carried out in the Cassini Grand Finale mission is insufficient to determine weak nonaxisymmetric gravitational moments because good subspacecraft-point coverage is lacking. The origin of the unexplained Saturnian gravity remains a puzzle. However, it is positively indicated by our simulations that future gravitational sounding is probably able to detect dynamo-related gravity when the subspacecraft-point coverage of a mission is sufficient. We suggest that the mission orbits be purposely designed into a near-polar orientation with a height of about 6000 km at periapsis and a moderate eccentricity of 0.5. A total POD tracking time of five months would enable the detection of the secular nonaxisymmetric gravitational moments that are caused by the deep convective dynamo of Saturn. The orbit strategy can facilitate engineering implementation by keeping the spacecraft marginally away from the Saturn radiation belt throughout the mission.