Size Of Convection Cells Research Articles

IMPACT OF AN ANISOTROPIC POROUS MEDIA ON THERMOBIOCONVECTION INSTABILITY IN THE PRESENCE OF GYROTACTICMICROORGANISMS AND HEATING FROM BELOW

The onset of thermobioconvection in a horizontal fluid layer saturated by gyrotactic microorganisms into an anisotropic porous medium is examined. The modeling of the governing equations considers heating from below, Darcy flow, and Boussinesq approximations along with the presence of gyrotactic microorganisms. The system of ordinary differential equations is obtained using linear stability analysis and the normal mode technique. The single-term Galerkin method casts the analytical solutions while the higher-order Galerkin technique is employed to compute the numerical solutions. The influence of the mechanical and thermal anisotropy parameters along with all bioconvection parameters on the onset of thermobioconvection are analytically as well as numerically discussed. It is perceived that bioconvection Rayleigh-Darcy number <i>Rb</i>, the gyrotactic number<i> G</i>, and Péclet number <i>Q</i> are to fast-forward the onset of convective motion. On the other hand, thermal anisotropy produces a stable system and acts to postpone the bioconvection pattern formulation. Mechanical anisotropy is found to have a destabilizing impact on the stability of the suspension and helps in the development of bioconvection. The enhancement of mechanical and thermal anisotropy is found to increase the size of bioconvective cells whereas the augmentation of the concentration of gyrotactic specie reduces the convective cell size.

Thermal instability analysis in magneto-hybrid nanofluid layer between rough surfaces with variable gravity and space-dependent heat source

The onset of thermal instability with hybrid nanoparticles Al2O3–Cu in nanofluid is investigated with the combined effects of variable gravity, variable heat source and Lorentz force in a porous medium. Its applications are in many areas like chemical engineering, geophysics, astrophysics, etc. Based on literature, many gravity variations are assumed in the present analysis, along with a space-dependent heat source/sink parameter that varies along the width of the channel. The finite difference-based Lobatto IIIa method has been applied to solve the system under no nanoparticle flux and rough boundary conditions, and approximate analytical results are generated for some special cases. The roughness parameters ([Formula: see text]), Darcy number (Da), gravity variation function ([Formula: see text]), and Chandrasekhar number (Q) delay the onset of convection and thus stabilize the system. It is also observed that an increase in the Lewis number Le, power index in variable heat source, and the nanoparticle Rayleigh concentration number Rn decreases the critical Rayleigh number [Formula: see text] which destabilizes the system, and increases the critical wave number, which enlarges the convection cell size. In the case of exponential variation ([Formula: see text]) in the gravity variation parameter, the system becomes stabilized due to a delay in the onset of convection. In addition, we have considered multilayer perceptron-artificial neural network (MLP-ANN) computation to predict the critical Rayleigh number as per function of important controlling parameters. The data set of 625 observations is chosen keeping 70% for testing, 15% for training and 15% for validation using efficient Levenberg−Marquardt back propagation algorithm with optimal accuracy measures i.e., root mean square deviation (RMSE), root mean relative error (RMRE) and [Formula: see text] (coefficient of determination). Finally, the regression plots are drawn that correlate, target and output data.

Morphology evolution of a melting solid layer above its melt heated from below

We numerically study the melting process of a solid layer heated from below such that a liquid melt layer develops underneath. The objective is to quantitatively describe and understand the emerging topography of the structures (characterized by the amplitude and wavelength), which evolve out of an initially smooth surface. By performing both two-dimensional (achieving Rayleigh number up to$Ra=10^{11}$) and three-dimensional (achieving Rayleigh number up to$Ra=10^9$) direct numerical simulations with an advanced finite difference solver coupled to the phase-field method, we show how the interface roughness is spontaneously generated by thermal convection. With increasing height of the melt the convective flow intensifies and eventually even becomes turbulent. As a consequence, the interface becomes rougher but is still coupled to the flow topology. The emerging structure of the interface coincides with the regions of rising hot plumes and descending cold plumes. We find that the roughness amplitude scales with the mean height of the liquid layer. We derive this scaling relation from the Stefan boundary condition and relate it to the non-uniform distribution of heat flux at the interface. For two-dimensional cases, we further quantify the horizontal length scale of the morphology, based on the theoretical upper and lower bounds given for the size of convective cells known from Wanget al.(Phys. Rev. Lett., vol. 125, 2020, 074501). These bounds agree with our simulation results. Our findings highlight the key connection between the morphology of the melting solid and the convective flow structures in the melt beneath.

Stability analysis of thermo-bioconvection flow of Jeffrey fluid containing gravitactic microorganism into an anisotropic porous medium

This paper presents a novel study on the stability of thermo-bioconvection due to gravitactic microorganisms into an anisotropic porous fluid layer saturated with Jeffrey liquid. A Jeffrey-Darcy model along with Boussinesq approximations is utilized. The field equations are treated with non-dimensionalization, linear stability analysis, and the normal mode technique to formulate a set of ordinary differential equations. These equations along with Robin boundary conditions are then analytically solved by employing the weighted residual Galerkin method utilizing the trigonometric trial functions. The traditional thermal Rayleigh-Darcy number Ra,c is obtained as a well-compiled function of the mechanical anisotropy parameter ξ, Jeffrey parameter γ, the thermal anisotropy parameter η, bioconvection Rayleigh-Darcy number Rb, and Péclet number Q, while it is independent from bioconvection Lewis number Lb. It is observed that mounting ξ and γ in between 0 to 1 hasten the formulation of bioconvection patterns and also enlarges the size of convective cells. The results demonstrate that increasing bioconvection Péclet number and microorganism concentration constitute an unstable system. η ranged between 0 to 1 has shown dual effect which is dominated by the concentration of gravitactic microorganism. For small microorganism concentration, augmenting thermal anisotropy strength stabilizes the system and increases the size of the convective cells. Mathematically, the stabilizing nature of η is bounded by the feasibility of the inequality (π2+δc2ξ)(1+γ)ξ>2Rbδc2(eQ−1)π2Q2(π2+δc2)(π2+Q2)(4π2+Q2). This study may find relevance in applications related to pharmaceutical, bio-mechanics, and in microbial enhanced oil recovery (MEOR). The experimental Ra,c value of measure 4π2 at critical wave number value δc=π is also regained as a limiting case from this study.

Ferroconvection In A Horizontal Darcy-Brinkman Porous Medium With Radiative Transfer

<p>The classical linear stability analysis is used to examine the effect of thermal radiation on the onset of Darcy-Brinkman ferroconvection. The boundaries of the fluid layer are treated as black bodies and the optical properties of the transparent ferromagnetic fluid are independent of the wave length of radiation. The fluid and solid matrix are assumed to be in local thermal equilibrium. Considering realistic boundary conditions, the principle of exchange of stabilities is shown to be valid and the critical values pertaining to the stationary instability are obtained by means of the higher order Galerkin method. It is observed that the basic temperature profile turns out to be exponential and symmetric as the radiative parameters increase and that the effect of thermal radiation is to delay the onset of Darcy- Brinkman ferroconvection. The destabilizing influence of magnetic forces is affected by the radiative parameters. The effect of magnetic, radiative and porous parameters on the convection cell size is also discussed.</p>

A Machine‐Learning‐Assisted Stochastic Cloud Population Model as a Parameterization of Cumulus Convection

AbstractA machine‐learning‐assisted stochastic cloud population model is coupled with the Advanced Research Weather Research and Forecasting (WRF) model to represent fluctuations in the cloud‐base mass flux associated with the life cycles and interactions among cumulus convection cells. In this cloud population model, the size distribution and the associated cloud‐base mass flux of the convective cells are related to their previous state and to the change in the total convective area via a transition function. The convective area tendency in turn is assumed to depend on the cloud‐base mass flux that is resolved by the host WRF model. The transition function is represented by a single hidden‐layer neural network trained by the evolution of convective cell size distributions in a 1‐km grid‐spacing WRF simulation run over the Australian Monsoon region. At every grid point of the host model, the cloud population model predicts the cell size and cloud‐base mass flux distributions from which a random sample of cells is fed to an entraining parcel model that calculates precipitation as well as the associated liquid water potential temperature and total moisture tendencies. These tendencies are averaged over the cells and provided to the host model. Several regional simulations are performed over tropical and midlatitude domains to test this as a potential approach to scale‐aware parameterization. It is shown that such an approach could be a new promising path to simulating realistic precipitation statistics and propagation of precipitation associated with the Madden‐Julian Oscillation while maintaining realistic depictions of the diurnal cycle over both land and ocean.

Combined Effects of Helical Force and Rotation on Stationary Convection of a Binary Ferrofluid in a Porous Medium.

This work studies the simultaneous effects of helical force, rotation and porosity on the appearance of stationary convection in a binary mixture of a ferrofluid and on the size of convection cells. We have determined the analytical expression of the Rayleigh number of the system as a function of the dimensionless parameters. The effect of each parameter on the system is studied. The consideration of the simultaneous effect of the basic characteristics made it possible to determine the evolution of the convection threshold in the ferrofluid and then the size of convection cells. The analyzes of the various results obtained allowed us to deduce whether the convection sets in quickly or with a delay when the various effects taken into account in the study are considered simultaneously.

Effects of thermodiffusion on Darcy–Brinkman convection in a rotating binary nanofluid saturating a porous layer

In this study, the onset of convection in a rotating horizontal porous layer saturated by a binary nanofluid was theoretically investigated under the influence of thermodiffusion and nanoparticles. To study the onset of convection, the Darcy–Brinkman model was employed for the porous medium, and the thermal Rayleigh number was derived analytically using linear stability analysis. Water–ammonia-based silver, copper, and alumina, three binary nanofluids, were considered, and the effect of nanoparticles on the stability of the system was analysed using addition factor analysis. The Brinkman model for viscosity and Bruggeman model under the mean field approach for thermal conductivity were used to study the impact of nanoparticles. Heat transport was examined by calculating the heat transfer coefficient. The effects of nondimensional parameters involved in binary nanofluids on the onset of convective instabilities are depicted pictorially. The dependence of the size of the convection cells on nondimensional parameters is also discussed. The Darcy–Taylor number decreases the size of convection cells, whereas the Darcy number increases the size of convection cells. The size of the convection cells is independent of the porosity of the medium, Lewis number, volume fraction of nanoparticles, Soret effect of nanoparticles, and the solute in binary nanofluids. Furthermore, the Darcy–Taylor number and porosity have stabilising effects, whereas the Darcy number, volume fraction of nanoparticles, and Lewis number have destabilising effects on the system. Soret effects of nanoparticles and solutes exhibit dual consequences on stability. They stabilise the binary nanofluid layer if δ4 < –1 and destabilise when δ4 > –1. Their effect is immaterial if δ4 = –1.

The effect of variable gravity on rotating Rayleigh–Bénard convection in a sparsely packed porous layer

AbstractThe effect of variable gravity on rotating convection in a sparsely packed porous layer is studied numerically. For gravity force variation, the linear, parabolic, cubic, and exponential functions are considered. Boundary conditions for the governing equations are considered to be either free or rigid. The normal mode method is employed, and the resulting eigenvalue problem is solved numerically for free–free and rigid–rigid boundaries using bvp4c in MATLAB R2020b. The influence of Darcy number (), gravity variation parameter (), and Taylor number () on the stability of the system is investigated graphically. It is confirmed that the gravity variation parameter and Taylor number delay the onset of convection and Darcy number enhances the onset of convection. The size of convection cells decreases on raising the variable gravity parameter and rotation parameter, while the Darcy number amplifies the size of convection cells. It is also observed that the system is stable for exponential gravity function and less stable for the cubic gravity function.

Classical Linear Stability Analysis of Energy Based Internally Heated Distributions on Bénard Porous Convection in a Micropolar Fluid Layer

The theoretical and numerical analysis is carried out on the effect of three types of configurations of Rayleigh-Bénard (RB) convection driven by the boundary combinations of Rigid-Rigid (R-R), Rigid-Free (R-F) and Free-Free (F-F). The RB convection models are distinguished by the three different temperature boundary conditions like: 1) RB1: lower and upper at fixed-temperature, 2) RB2: lower and upper with fixed-heat flux, or perfectly insulating and 3) RB3: bottom surface is fixed-temperature and top surface is fixed-heat flux. A Galerkin-type is based on the weighted residual method (WRM) which has been used to obtain the eigenvalue for gravity thermal Rayleigh number. It is noted that the porous medium of Darcy parameter and spin diffusion (couple stress) parameter N3 is to hasten coupling parameter N1 and micropolar heat conduction parameter N5 is to delay the onset of convection. Further, increase in the value of N1, N5, and as well as decrease in N3 is to diminish the size of convection cells.

The Coriolis Effect on Thermal Convection in a Rotating Sparsely Packed Porous Layer in Presence of Cross-Diffusion

The effect of rotation and cross-diffusion on convection in a horizontal sparsely packed porous layer in a thermally conducting fluid is studied using linear stability theory. The normal mode method is employed to formulate the eigenvalue problem for the given model. One-term Galerkin weighted residual method solves the eigenvalue problem for free-free boundaries. The eigenvalue problem is solved for rigid-free and rigid-rigid boundaries using the BVP4c routine in MATLAB R2020b. The critical values of the Rayleigh number and corresponding wave number for different prescribed values of other physical parameters are analyzed. It is observed that the Taylor number and Solutal Rayleigh number significantly influence the stability characteristics of the system. In contrast, the Soret parameter, Darcy number, Dufour parameter, and Lewis number destabilize the system. The critical values of wave number for different prescribed values of other physical parameters are also analyzed. It is found that critical wave number does not depend on the Soret parameter, Lewis number, Dufour parameter, and solutal Rayleigh number; hence critical wave number has no impact on the size of convection cells. Further critical wave number acts as an increasing function of Taylor number, so the size of convection cells decreases, and the size of convection cells increases because of Darcy number.

The onset of convection in liquid with the free surface cooled from above: Influence of the surface behavior on the size and formation time of critical perturbations

The onset of convection in an initially homogeneous liquid layer cooled from above is investigated by means of a non-normal approach. This method is based on the analysis of the temporal evolution of small perturbations. The most amplified perturbation and the moment, when convection can be observed, are determined. Experimental measurements are performed for a layer of distilled water cooled by evaporation. Instantaneous surface temperature fields are obtained using infrared thermography. The effect of the surface mobility on the size and onset time of convective cells is examined. The comparison of experimental results with numerical simulations for different boundary conditions reveals the presence of a film of adsorbed contaminants on the surface of distilled water, which corresponds to the no-slip condition. In the presence of the film, boundary conditions for cooling from above and heating from below become the same, and the obtained results agree with the experimental data available for a liquid layer with a heated bottom. As the layer depth increases, the onset time and the average horizontal wavenumber of convective cells become independent from the layer depth. The condition for the transition to a deep water approximation is determined by the surface heat flux and thermophysical parameters of the liquid.

The Horton–Rogers–Lapwood problem in a Jeffrey fluid influenced by a vertical magnetic field

In this work, the impact of a magnetic field on the onset of the Jeffrey fluid convection through a porous medium is investigated theoretically. The layer of Jeffrey fluid is heated from below and is operated by a consistent upright magnetic field. Using the normal mode procedure, a dispersion equation is obtained analytically and this dispersion relation is utilized to derive the critical conditions for the onset of stationary and oscillatory patterns of convection. The results reveal that the stability of the system diminished with the augmentation of the Jeffrey parameter, while an opposite result is obtained with magnetic field parameters (magnetic Chandrasekhar–Darcy number and magnetic Prandtl number). The size of convective cells decreases with Jeffrey and magnetic field parameters. It is also found that the existence of a magnetic field indicates the possibility of the survival of the oscillatory mode of convection.

Cattaneo-LTNE Effects on the Stability of Brinkman Convection in an Anisotropic Porous Layer

The stability of Brinkman local thermal nonequilibrium anisotropic porous convection under the impact of Cattaneo law of heat conduction in solid is investigated. In the analysis, anisotropies in permeability and thermal (solid and fluid phases) conductivities are highlighted. Condition for stationary onset and oscillatory onset is obtained by carrying out linear instability analysis. A novel result is that the instability occurs through oscillatory mode against the stationary convection perceived in the absence of Cattaneo effect. The relative magnitudes of governing parameters on the initiation of oscillatory instability are delineated in detail. The thermal and mechanical anisotropies inflict stabilizing and destabilizing effects on the onset, respectively. The influence of mechanical anisotropy, thermal anisotropy of fluid, thermal relaxation time parameters and the Darcy number is to broaden the size of convection cells whereas thermal anisotropy of the solid and the Darcy-Prandtl number demonstrate a mixed behaviour. A first order amplitude equation is derived separately for steady and overstable modes by performing a weak nonlinear stability analysis using a modified multiscale method. Depending on the values of governing parameters, it is seen that the stationary mode bifurcates subcritically and supercritically, while the oscillatory mode always bifurcates supercritically.

Resolution Dependence and Subfilter-Scale Motions in Idealized Squall-Line Simulations

Abstract In this paper, the sensitivity of idealized squall-line simulations to horizontal resolution, subgrid turbulence mixing scheme, and subfilter-scale motion is discussed. Inconsistent results from numerical simulations of convective systems have suggested that there are issues with the behavior of the subgrid turbulent mixing parameterizations with increasing resolution that still need to be understood. WRF is used to perform large-eddy simulation of an idealized squall line with horizontal grid spacings of 4 km, 2 km, 1 km, 500 m, and 250 m. While 4 km grid spacing is able to produce the general structure of the squall line, higher-resolution simulations produce more detailed structures. Individual convective cell size decreases, the maximum cloud top height increases, and the subgrid turbulence kinetic energy (TKE) ratio decreases as resolution increases. As found in past studies, 4 km grid spacing is not recommended as it contains an unreasonable amount of subgrid TKE, is not sufficient to resolve the large energy-containing eddies, and may even suppress propagation of the squall line. While horizontal resolution of 1 km can produce a squall line, there are several discrepancies between the 1 km case and higher resolutions, including trailing banded structures and inhibited three-dimensionalization. These issues at 1 km resolution are investigated by examining the subfilter energy transfer for the highest-resolution simulation filtered to a horizontal scale of 1 km. The subfilter energy transfer rate at a scale of 1 km is dominated by the streamwise and shear components. While dissipation dominates the transfer, a significant amount of backscatter also exists, which is not represented by most subgrid models.

Linear stability analysis of mixed convection flow in a horizontal channel filled with nanofluids

AbstractThe convective instability driven by buoyancy in the Poiseuille–Rayleigh–Bénard flow through two infinite parallel horizontal plates filled with nanofluids is investigated using linear stability analysis. We considered water‐based nanofluids with different volume fractions of aluminum () and silver () nanoparticles. A spectral collocation method founded on Chebyshev polynomials is implemented and the obtained algebraic eigenvalue problem is solved. In this study, we have numerically determined the critical Rayleigh number of the onset of longitudinal and transversal rolls and the results are represented in the form of marginal stability curves. Critical wave numbers that describe the size of convective cells in the flow are also presented, analyzed, and compared with those of the Poiseuille–Rayleigh–Bénard flow without nanoparticles. The effects of the type and nanoparticle volume fractions on the onset of both longitudinal and transversal rolls are investigated.

Thermal instability of an Oldroyd-B fluid-saturated porous layer: implications of pressure gradient and LTNE temperatures

A local thermal nonequilibrium model is used to investigate the instability of an Oldroyd-B fluid-saturated horizontal layer of porous medium by imposing a constant pressure gradient in the horizontal direction and maintaining a constant temperature difference between the boundaries. The flow in the porous medium is studied by a modified Darcy–Oldroyd-B model. The problem has been transformed into a generalized complex eigenvalue problem and solved numerically by utilizing the Galerkin method. The pressure gradient and/or the viscoelasticity of the fluid instill oscillatory instability. The influence of constant horizontal pressure gradient is to hasten the onset of oscillatory convection: a result of contrast noticed in Newtonian fluids. The impact of constant horizontal pressure gradient is to increase the critical frequency of oscillations and to increase the size of convection cells. Besides, the effect of viscoelastic parameters on the oscillatory onset diminishes in the presence of pressure gradient. For the Maxwell fluid, instability sets in earlier compared to an Oldroyd-B fluid. The numerical results obtained under the limiting case are shown to be in excellent agreement with the published ones.

A Machine Learning Assisted Development of a Model for the Populations of Convective and Stratiform Clouds

AbstractTraditional parameterizations of the interaction between convection and the environment have relied on an assumption that the slowly varying large‐scale environment is in statistical equilibrium with a large number of small and short‐lived convective clouds. They fail to capture nonequilibrium transitions such as the diurnal cycle and the formation of mesoscale convective systems as well as observed precipitation statistics and extremes. Informed by analysis of radar observations, cloud‐permitting model simulation, theory, and machine learning, this work presents a new stochastic cloud population dynamics model for characterizing the interactions between convective and stratiform clouds, with the goal of informing the representation of these interactions in global climate models. Fifteen wet seasons of precipitating cloud observations by a C‐band radar at Darwin, Australia are fed into a machine learning algorithm to obtain transition functions that close a set of coupled equations relating large‐scale forcing, mass flux, the convective cell size distribution, and the stratiform area. Under realistic large‐scale forcing, the derived transition functions show that, on the one hand, interactions with stratiform clouds act to dampen the variability in the size and number of convective cells and therefore in the convective mass flux. On the other, for a given convective area fraction, a larger number of smaller cells is more favorable for the growth of stratiform area than a smaller number of larger cells. The combination of these two factors gives rise to solutions with a few convective cells embedded in a large stratiform area, reminiscent of mesoscale convective systems.

The Relationship of Cloud Number and Size With Their Large‐Scale Environment in Deep Tropical Convection

AbstractAccurately representing the properties and impact of tropical convection in climate models requires an understanding of the relationships between the state of a convective cloud ensemble and the environment it is embedded in. We investigate this relationship using 13 years of radar observations in the tropics. Specifically, we focus on convective cell number and size and quantify their relationship to atmospheric stability, midtropospheric vertical motion and humidity. We find several key convective states embedded in their own unique environments. The most area‐averaged rainfall occurs with a moderate number of moderate size convective cell in an environment of high humidity, strong vertical ascent, and moderate convective available potential energy (CAPE) and convective inhibition (CIN). The strongest rainfall intensities are found with few large cells. Those exist in a dry and subsiding environment with both high CAPE and CIN. Large numbers of convective cells are associated with small CAPE and CIN, weak ascent, and a moist midtroposphere.

Dynamical investigation of a thickening ice-shell: Implications for the icy moon Europa

Current astrobiological exploration of the outer solar system is largely driven by understanding planetary ice-ocean systems such as those of Europa and Enceladus. The ice-shell thickness that affects the dynamics of the ice-ocean system is determined by the balance between heat loss via convection and conduction, and the heat production via tidal dissipation and radiogenic decay. In this study, we investigate how ice-shells of such ocean moons grow, and how convection inside them evolves as the system cools. We perform geodynamical calculations to investigate the ice-shell thickness and growth rate as the system cools from a warm initial condition. We study both diffuse and localized end member modes of tidal dissipation within the ice-shell. We find that as the ice-shell cools and thickens, there is a reconfiguration of the convection patterns, increasing the size of convection cells that leads to a relatively significant increase in the ice-shell growth rate.