Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userOff-center gravity induces large-scale flow patterns in spherical Rayleigh-Benard
218
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Inspired by the hemispherical asymmetry observed in the Earths inner core, we perform direct numerical simulations to study the effect of the gravity center offset in spherical Rayleigh-Benard convection. We find that even a minimal shift of the gravity center has a pronounced influence on the flow structures. When the gravity center is shifted towards the South, the co-latitudinal buoyancy component creates an energetic jet on the Northern side of the inner sphere that is directed towards the outer sphere. As a result, a large-scale meridional circulation is formed. However, surprisingly, the global heat flux is not affected by the changes in the large-scale flow organization induced by the gravity center offset. Our results suggest that the hemispherical core asymmetry is key to model the flow phenomena in the Earths outer core and mantle.
rate research
Read More
We analyse the nonlinear dynamics of the large scale flow in Rayleigh-Benard convection in a two-dimensional, rectangular geometry of aspect ratio $Gamma$. We impose periodic and free-slip boundary conditions in the streamwise and spanwise directions, respectively. As Rayleigh number Ra increases, a large scale zonal flow dominates the dynamics of a moderate Prandtl number fluid. At high Ra, in the turbulent regime, transitions are seen in the probability density function (PDF) of the largest scale mode. For $Gamma = 2$, the PDF first transitions from a Gaussian to a trimodal behaviour, signifying the emergence of reversals of the zonal flow where the flow fluctuates between three distinct turbulent states: two states in which the zonal flow travels in opposite directions and one state with no zonal mean flow. Further increase in Ra leads to a transition from a trimodal to a unimodal PDF which demonstrates the disappearance of the zonal flow reversals. On the other hand, for $Gamma = 1$ the zonal flow reversals are characterised by a bimodal PDF of the largest scale mode, where the flow fluctuates only between two distinct turbulent states with zonal flow travelling in opposite directions.
Direct numerical simulations are employed to reveal three distinctly different flow regions in rotating spherical Rayleigh-Benard convection. In the low-latitude region $mathrm{I}$ vertical (parallel to the axis of rotation) convective columns are generated between the hot inner and the cold outer sphere. The mid-latitude region $mathrm{II}$ is dominated by vertically aligned convective columns formed between the Northern and Southern hemispheres of the outer sphere. The diffusion-free scaling, which indicates bulk-dominated convection, originates from this mid-latitude region. In the equator region $mathrm{III}$ the vortices are affected by the outer spherical boundary and are much shorter than in region $mathrm{II}$. Thermally driven turbulence with background rotation in spherical Rayleigh-Benard convection is found to be characterized by three distinctly different flow regions. The diffusion-free scaling, which indicates the heat transfer is bulk-dominated, originates from the mid-latitude region in which vertically aligned vortices are stretched between the Northern and Southern hemispheres of the outer sphere. These results show that the flow physics in rotating convection are qualitatively different in planar and spherical geometries. This finding underlines that it is crucial to study convection in spherical geometries to better understand geophysical and astrophysical flow phenomena.
By utilizing diffusion maps embedding and transition matrix analysis we investigate sparse temperature measurement time-series data from Rayleigh--Benard convection experiments in a cylindrical container of aspect ratio $Gamma=D/L=0.5$ between its diameter ($D$) and height ($L$). We consider the two cases of a cylinder at rest and rotating around its cylinder axis. We find that the relative amplitude of the large-scale circulation (LSC) and its orientation inside the container at different points in time are associated to prominent geometric features in the embedding space spanned by the two dominant diffusion-maps eigenvectors. From this two-dimensional embedding we can measure azimuthal drift and diffusion rates, as well as coherence times of the LSC. In addition, we can distinguish from the data clearly the single roll state (SRS), when a single roll extends through the whole cell, from the double roll state (DRS), when two counter-rotating rolls are on top of each other. Based on this embedding we also build a transition matrix (a discrete transfer operator), whose eigenvectors and eigenvalues reveal typical time scales for the stability of the SRS and DRS as well as for the azimuthal drift velocity of the flow structures inside the cylinder. Thus, the combination of nonlinear dimension reduction and dynamical systems tools enables to gain insight into turbulent flows without relying on model assumptions.
For rapidly rotating turbulent Rayleigh--Benard convection in a slender cylindrical cell, experiments and direct numerical simulations reveal a boundary zonal flow (BZF) that replaces the classical large-scale circulation. The BZF is located near the vertical side wall and enables enhanced heat transport there. Although the azimuthal velocity of the BZF is cyclonic (in the rotating frame), the temperature is an anticyclonic traveling wave of mode one whose signature is a bimodal temperature distribution near the radial boundary. The BZF width is found to scale like $Ra^{1/4}Ek^{2/3}$ where the Ekman number $Ek$ decreases with increasing rotation rate.
We studied the properties of the large-scale circulation (LSC) in turbulent Rayleigh-Benard (RB) convection by using results from direct numerical simulations in which we placed a large number of numerical probes close to the sidewall. The LSC orientation is determined by either a cosine or a polynomial fit to the azimuthal temperature or azimuthal vertical velocity profile measured with the probes. We study the LSC in Gamma=D/L=1/2 and Gamma=1 samples, where D is the diameter and L the height. For Pr=6.4 in an aspect ratio Gamma=1 sample at $Ra=1times10^8$ and $5times10^8$ the obtained LSC orientation is the same, irrespective of whether the data of only 8 or all 64 probes per horizontal plane are considered. In a Gamma=1/2 sample with $Pr=0.7$ at $Ra=1times10^8$ the influence of plumes on the azimuthal temperature and azimuthal vertical velocity profiles is stronger. Due to passing plumes and/or the corner flow the apparent LSC orientation obtained using a cosine fit can result in a misinterpretation of the character of the large-scale flow. We introduce the relative LSC strength, which we define as the ratio between the energy in the first Fourier mode and the energy in all modes that can be determined from the azimuthal temperature and azimuthal vertical velocity profiles, to further quantify the large-scale flow. For $Ra=1times10^8$ we find that this relative LSC strength is significantly lower in a Gamma=1/2 sample than in a Gamma=1 sample, reflecting that the LSC is much more pronounced in a Gamma=1 sample than in a Gamma=1/2 sample. The determination of the relative LSC strength can be applied directly to available experimental data to study high Rayleigh number thermal convection and rotating RB convection.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
