Onset Of Convection Research Articles

Rapidly rotating self-gravitating Boussinesq fluid. IV. Onset of multimodal thermal convection influenced by oblate spheroidal geometry

Rapidly rotating self-gravitating Boussinesq fluid. IV. Onset of multimodal thermal convection influenced by oblate spheroidal geometry

Effects of rotation and chemical reactions on an electroconvection in Maxwell dielectric nanofluids within anisotropic porous media

ABSTRACT This study explores the complex interactions between rotation, chemical reactions, and electroconvection in Maxwell dielectric nanofluids within anisotropic porous media. The research aims to elucidate how these factors influence the heat transfer efficiency and fluid dynamics under the influence of external alternating current (AC) electric fields. The normal mode method is employed to analyse the stability of the system, allowing for the examination of oscillatory modes and their growth rates. By introducing perturbations in the physical parameters, the study derives a set of ordinary linear differential equations that characterize the system's response to external influences. The coupled differential equations were solved using the Galerkin approach for first approximation while meeting the necessary boundary conditions. Analytical solution of the representative equation for stress-free boundary states yields Rayleigh number formulas for nonoscillatory and oscillatory mode occur. Oscillatory modes are seen for both bottom and top-heavy nanoparticle distributions. The electric Rayleigh number, thermal Prandtl number, and stress relaxation parameter increases, whereas the Brinkman-Darcy number delays the onset of stationary and oscillatory convection. The study finds that positive concentration Rayleigh numbers stabilize the system, while negative ones lead to instability. Additionally, it demonstrates that external alternating current electric fields influence convection behavior and provides formulas for critical Rayleigh numbers, enhancing our understanding of fluid interactions in various engineering and technological applications.

Coherent flow structures and magnetic field patterns in rotating spherical shell convective dynamos: A data-driven approach

The Earth's outer core dynamics involve convective fluid motion generating an observable geomagnetic field. The velocity and magnetic fields exhibit characteristic spatiotemporal features possessing geophysical significance for which extensive datasets are available from direct observations and computational simulations. This study demonstrates the robustness of proper orthogonal decomposition (POD), a data-driven technique, in detecting prominent and relevant features in these datasets. Improvising on previous practices, the POD efficiently detects infinitesimal instabilities at the onset of convection, providing an accurate and objective methodology to determine the convective threshold, even for heterogeneous buoyancy forcing. Time evolution of paired, phase-shifted modes efficiently reconstructs the azimuthally drifting of traveling wave instabilities. Simultaneously reduced order modeling of velocity components clearly distinguish the equatorial and polar coherent flow structures. Supercritical convection-driven magnetic field data over long periods, generated using numerical simulations, produce dominant modes that are more accurately representative of time-averaged patterns than geocentric axial dipole patterns. Moreover, the quantitative significance of the dominant modes determines the extent of dimensional reduction complementing established diagnostics for dipolarity. Finally, analysis of observational geomagnetic field data reveals long-lived dominant patterns influenced by thermal core–mantle interaction consistent with numerical models employing tomographic heat flux boundary conditions in present as well as previous studies.

A Simple Model for the Emergence of Relaxation‐Oscillator Convection

AbstractEarth's tropics are characterized by quasi‐steady precipitation with small oscillations about a mean value, which has led to the hypothesis that moist convection is in a state of quasi‐equilibrium (QE). In contrast, very warm simulations of Earth's tropical convection are characterized by relaxation‐oscillator‐like (RO) precipitation, with short‐lived convective storms and torrential rainfall forming and dissipating at regular intervals with little to no precipitation in between. We develop a model of moist convection by combining a zero‐buoyancy model of bulk‐plume convection with a QE heat engine model, and we use it to show that QE is violated at high surface temperatures. We hypothesize that the RO state emerges when the equilibrium condition of the convective heat engine is violated, that is, when the heating rate times a thermodynamic efficiency exceeds the rate at which work can be performed. We test our hypothesis against one‐ and three‐dimensional numerical simulations and find that it accurately predicts the onset of RO convection. The proposed mechanism for RO emergence from QE breakdown is agnostic of the condensable, and can be applied to any planetary atmosphere undergoing moist convection. To date, RO states have only been demonstrated in three‐dimensional convection‐resolving simulations, which has made it seem that the physics of the RO state requires simulations that can explicitly resolve the three‐dimensional interaction of cloudy plumes and their environment. We demonstrate that RO states also exist in single‐column simulations of radiative‐convective equilibrium with parameterized convection, albeit in a different surface temperature range and with much longer storm‐free intervals.

Worldwide consequences of a mid-Holocene cold event in the Nordic Seas

The present interglacial is a relatively warm and stable period, especially compared to the preceding glacial time. However, the Holocene has seen the emergence of several remarkable cold events, some with worldwide consequences. Leveraging marine records from the Nordic Seas, we provide the first detailed account of a cold event centered around 6.8 ka BP. Utilizing paleoceanographic proxies and advanced modeling, we unveil a distinct subsurface water cooling, associated with a stepwise increase in sea-ice cover in the eastern Fram Strait. Our findings emphasize the role of Greenland Sea deep convection onset and the subsequent westward shift in Atlantic Water flow, enabling sea-ice advection from the Barents Sea. The heightened sea-ice cover weakened Atlantic Water advection, perturbing thermohaline circulation in the eastern Nordic Seas. These perturbations propagated worldwide, affecting North Atlantic deep-water circulation, inducing widespread hemispheric cooling, shifting the Intertropical Convergence Zone southward, and weakening the East Asian monsoon. Incorporating results from the Transient simulations of Climate Evolution of the last 21,000 years (TraCE-21ka) supports and augments proxy-based paleoreconstructions, underscoring sea-ice dynamics and ocean circulation's critical influence. This study highlights the potential for localized cold events within ostensibly warm climatic intervals. It underscores the need to comprehend their mechanisms for precise climate predictions and informed policymaking toward a sustainable future.

Heat transport enhancement by rotating bottom endwall in a cylindrical Rayleigh–Bénard convection

Rotating thermal convection, commonly encountered in natural and industrial environments, is typically influenced by both buoyancy forces and boundary rotation. In this study, we conduct direct numerical simulations to explore the effect of rotating bottom on the flow structure and heat transport of Rayleigh–Bénard convection (RBC) in a cylindrical cavity. This cavity has a radius-to-height ratio of 1 and is filled with an incompressible fluid with a Prandtl number of 0.7. Our results show that the axisymmetric convection pattern, observed in RBC for Ra∈[4000,8000] without rotation, transitions into a double roll structure at low rotating speeds (ω), while for Ra≤4000, the pattern remains axisymmetric, independent of ω. We then focus on the impact of bottom rotation on heat transport in the axisymmetric regime. Based on the variation in the Nusselt number (Nu) with ω, two distinct regimes are identified: a convection-dominated regime at low ω, where Nu closely resembles that of standard RBC, and a rotation-dominated regime at high ω, where strong shear induced by the rotating bottom intensifies the meridional circulation, significantly boosting global heat flux. The critical rotating speed, ω*, marking the transition between these regimes, follows different power-law relations below and above the buoyant convection onset (Rac): ω*∼Ra−0.64 for Ra<Rac and ω*∼Ra0.33 for Ra>Rac. As ω increases, the exponents for Nu∼Raλ and Re∼Raγ evolve before converging to λ≈0.3 and γ=0.5, respectively. Scaling laws for Nu and Re as functions of ω and Ra in the rotation-dominated regime are finally derived: Nu∼Ra0.3ω0.64 and Re∼Ra0.5ω.

On the onset of stationary convection on Jeffrey nanofluid layer saturated with a porous medium: Brinkman model

In this paper, we investigate the onset of convection in a Jeffrey nanofluid layer saturated with the porous medium using Darcy-Brinkmann model. Normal mode analysis and Galerkin type weighted residual method (GWRM) are used to analyse conservation equations. Effects of Brownian motion and thermophoresis are taken into account in the Jeffrey nanofluid model. The Buongiorno model deployed for nanoparticles incorporates the influences of thermophoresis and Brownian motion. Three cases of free-free, rigid-rigid and rigid-free boundaries are considered. For stationary convection, the effects of Darcy number, Jeffrey parameter, Lewis number, nanoparticle Rayleigh number, porosity and modified diffusivity ratio for all the above mentioned boundary conditions are investigated analytically and graphically. The numerical computed values of stationary thermal Rayleigh number are presented graphically for three distinct combinations of boundary conditions. The study is of great significance in many different areas such as automotive, pharmaceutical, geophysics, soil sciences, food processing, oceanography, limnology, etc., and excellent coincidence is found regarding the present paper and earlier published work.

Vorticity skewness of finite-amplitude rapidly rotating Rayleigh–Bénard convection

Rotating Rayleigh–Bénard convection denotes the convection between a warm plate and a cold plate in a rotating environment. It is a classic model for understanding convective vortices in the atmosphere and ocean. The influence of background rotation on fluid inertia breaks the symmetry between cyclones and anticyclones. Such a symmetry breaking could be represented by vorticity skewness, which still lacks a systematic theory. Rapidly rotating convection with stress-free boundaries and unit Prandtl number is a convenient starting point. The investigation starts from the convective onset stage, where the vortices grow stationarily. Asymptotic analysis shows that the volumetric vorticity skewness $S$ is produced by the interaction between the $n=0,1$ and $n=1,2$ vertical eigenmodes. The $n=0$ (barotropic) mode contributes positively to $S$ mainly by stretching the vertical relative vorticity, an ageostrophic effect. The $n=2$ mode makes a minor negative contribution to $S$ by preferentially intensifying the outflow over the inflow, a non-hydrostatic effect. The theory predicts $S$ to be proportional to the global Rossby number defined with the volumetric standard deviation of vorticity, ${Ro_g}$ . The proportional factor does not depend on the Rayleigh and Ekman numbers, agreeing with direct numerical simulations. Then the system enters the equilibrium stage. The stretching of vertical vorticity still contributes to $S$ dominantly. At ${Ro_g}\gtrsim 0.5$ , the emergent unsteady flow significantly suppresses the asymmetry between the inflow and outflow strength, and weakens its influence on $S$ .

The role of temperature-dependent solubility in the stability of thermohaline convection within a Voigt-fluid layer

The study focuses on both linear and weakly nonlinear stability analyses of thermohaline convection within a Voigt-fluid layer, considering the effects of temperature-dependent solubility. Analytical methods are employed to derive conditions for the onset of both stationary and oscillatory convection. The linear stability analysis is performed using normal mode analysis to explore how various physical parameters influence the initiation of convection. Notably, unlike Newtonian fluids, the Navier-Stokes-Voigt fluid suppresses the typical quasiperiodic bifurcation from a steady state. To gain deeper insight into the onset of convection, a weakly nonlinear stability analysis is conducted using a modified perturbation method, leading to the Ginzburg-Landau equation. This reveals the potential for subcritical instability, a phenomenon not fully captured by linear analysis alone. Additionally, the study examines how different physical parameters affect convective heat and mass transfer, with findings that align with previous studies in specific limiting cases.

Onset of double-diffusive convection in a Poiseuille flow with a uniform internal heat source

The linear stability analysis of the onset of double-diffusive convection in a Poiseuille flow system is investigated. In addition, a volumetric uniform internal heat source is taken into account. In this problem, the horizontal fluid channel is bounded by two plates which are isothermal and isosolutal. The governing parameters are thermal Rayleigh number RaT, solutal Rayleigh number Ras, internal heat source parameter RaI, Prandtl number Pr, and Reynolds number Re. The eigenvalue problem arising from the linear perturbed system of equations is solved numerically using the Chebyshev–Tau method coupled with the QZ algorithm. It is found that the positive solutal Rayleigh number Ras destabilizes the system. Furthermore, it is observed that an increase in the Prandtl number Pr stabilizes the system. Additionally, at Ras = −60, the critical values of the thermal Rayleigh number Rac decreases with R=Re cos ϕ up 2; and increases with R beyond R=2.

Perspectives on local thermal non-equilibrium (LTNE) Darcy–Bénard convection: Variable permeability and viscosity effects

The interplay between variations in permeability and viscosity on the onset of local thermal non-equilibrium in Darcy–Bénard convection has been investigated. Specifically, permeability is modeled as decreasing linearly with depth, while viscosity decreases exponentially. The validity of the principle of exchange of stabilities is confirmed. A linear instability analysis of the quiescent state is conducted through normal mode decomposition of disturbances, with threshold values for instability onset computed numerically using the Galerkin method. The individual and combined effects of increasing the variable permeability and viscosity parameters on the instability characteristics of the system are examined in detail, highlighting both commonalities and distinctions. It is observed that increasing each parameter individually hastens the onset of convection. However, their combined influence produces both stabilizing and destabilizing effects under certain parametric conditions. In all scenarios, an increase in the scaled interphase heat transfer coefficient consistently delays the onset of convection, whereas a higher ratio of porosity-modified conductivities has the opposite effect. Furthermore, the size of the convection cells remains unchanged at the extreme values of the scaled interphase heat transfer coefficient.

Triple-diffusive instabilities in Ellis fluid-saturated porous layers: Dynamics of oscillatory convection

Triple-diffusive convection in Ellis fluid-saturated porous layers has a wide array of real-world applications, including enhanced oil recovery, optimized geothermal energy extraction, and improved food processing and drug delivery systems. It also plays a crucial role in environmental management, particularly in controlling groundwater contamination and maintaining soil health by modeling pollutant transport and nutrient dynamics. This study explores the onset of convection in an Ellis fluid-saturated porous layer, influenced by three stratifying agents with differing diffusivities. A modified Darcy porous medium, salted from below, is subjected to horizontal throughflow driven by a prescribed pressure gradient. Through normal mode analysis, a linear stability analysis is conducted, resulting in explicit threshold conditions for the onset of convection. The findings reveal that convection begins with oscillatory motion, driven by the combined effects of the pressure gradient and solute concentration gradients. Notably, the study uncovers the emergence of disconnected, closed, heart-shaped oscillatory neutral curves, indicating the presence of three critical values of the solutal Darcy-Rayleigh number required to establish linear instability criteria and novel discovery for an Ellis fluid-saturated porous medium. Moreover, the results show that increasing the solutal Darcy-Rayleigh number and the Ellis power-law index stabilizes the system, while a higher Darcy-Ellis number leads to destabilization. The results obtained in the limiting cases are found to be consistent with those reported in previous studies.

Impact of temperature-dependent viscosity on linear and weakly nonlinear stability of double-diffusive convection in viscoelastic fluid

The impact of temperature-dependent viscosity on the double-diffusive viscoelastic convective fluids is investigated, with applications in heat transfer, polymer processing, food industry, biomedical engineering, etc. Both linear and weakly nonlinear analyses are carried out to determine the stability of fluids using the Oldroyd-B model. Analytical criteria for the onset of linear stationary and oscillatory convection are derived. The effects of rheological parameters, linearly and exponentially varying viscosity, salinity Rayleigh number and Prandtl number on the system’s stability are investigated. Linear stability analysis reveals that the interaction between thermal and solute diffusions with rheological parameters favours oscillatory convection over stationary convection. In weakly nonlinear theory, a power series expansion derives a Landau amplitude equation, allowing heat and mass transfer analysis in viscoelastic fluids with temperature-dependent viscosity. Numerical results highlight the effects of variable viscosity on heat and mass transfer rates, represented by Nusselt and Sherwood numbers. Further, the weakly non-linear stability analysis evaluates the impact of the Prandtl number, rheological parameters and salinity Rayleigh number on heat and mass transfer rates. These findings are compared with existing results to validate and enhance our understanding of fluid behaviour under different conditions.

Onset of Darcy–Brinkman convection with thermal anisotropy in an inclined porous layer

In this article, we study the linear instability and the nonlinear stability (through energy functional) analyses of thermal convection in an inclined Darcy–Brinkman porous layer considering uniformly heated horizontal rigid, impermeable walls from below and above. The effects of a uniform internal heat source and anisotropy in effective thermal diffusivity on heat transfer are also considered. Heating the porous layer from below yields the temperature gradient, influencing the buoyancy and making the convection happen. This temperature gradient also impacts the base state. The basic solution for velocity incorporates both hyperbolic and polynomial functions, significantly increasing the complexity of linear and nonlinear analyses. The Chebyshev-tau method, together with the QZ algorithm, is used to solve the linear and nonlinear perturbed system of equations numerically. The region of subcritical instability is obtained by comparing the linear and nonlinear thresholds for the longitudinal and transverse rolls, respectively. We found that perturbations for longitudinal and transverse rolls do not grow after inclination is more than 30.3° and 31.3°, respectively. It has been noted that in transverse roll scenarios, the flow becomes stabilized when the inclination angle, ϕ, is equal to or exceeds 60°, where ϕ plays a leading role in surpassing the impact of internal heating. However, when the inclination angle is ϕ<60°, then internal heating dominates and destabilizes the flow. For the longitudinal rolls, the internal heating dominates the whole range of ϕ, destabilizing the system. Furthermore, it can be seen that the Darcy number (Da) and the anisotropic thermal diffusivity (ξ) delay the onset of convection.

ANALYTIC STUDY OF THERMOHALINE CONVECTIVE STABILITY IN A COUPLE-STRESS FLUID

This work investigates nonlinear analysis for thermohaline convective stability in a steady, viscous, incompressible couple-stress fluid by performing a generalized energy method. It is observed that the linear and nonlinear threshold that reflects the physics of the onset of convection is the same. The couple stress and solute gradient are seen to have a stabilizing impact on the system.

Effect of noninertial acceleration on heat transfer by Rayleigh–Bénard magnetoconvection: Exploring nonlinear dynamics

AbstractBuoyancy‐driven Rayleigh–Bénard convection in the presence of a magnetic field, rotation, and temperature‐dependent viscosity has applications in the field of crystal growth, space laboratory experiments, and atmospheric convection. It also has potential applications in heat transfer and magnetohydrodynamics, which can occur in planetary and stellar interiors. The present work aims to study the combined effect of magnetic fields and rotation on the onset of Rayleigh–Bénard convection in temperature‐dependent viscosity Newtonian liquids with internal heat sources/sinks. Both linear and weak nonlinear stability analyses of convection are performed in the problem. The minimal representation of the Fourier series for the stream function and the magnetic potential allows us to derive the analytical expression for the thermal Rayleigh number () and the generalized Lorenz model. In linear theory, the critical Rayleigh number and the wave number are tabulated for different values of the Chandrasekhar number (), the Taylor number (), and the thermorheological parameter (), and the onset of stability is analyzed. It is found that the instability manifests at when for stress‐free and isothermal boundaries. In nonlinear theory, the generalized Lorenz model obtained is not amenable to analytical treatment; therefore, the classical fourth‐order Runge–Kutta method is applied to solve the Lorenz model. It is found that the internal Rayleigh number, the thermorheological parameter, and the Taylor number influence the onset of convection and heat transfer coefficient. It is also demonstrated that the joint increase in rotational force and magnetic field strength stabilizes the system strongly, thereby reducing heat transfer. However, increasing the heat source and the variable viscosity parameter have antagonistic influences.

Temperature Condition Impact on the Onset of Rayleigh-Benard Convection in a Binary Fluid Saturated Anisotropic Porous Layer

Rayleigh-Benard convection in a saturated anisotropic porous media is investigated numerically. The temperature-dependent viscosity effect was applied to the double-diffusive binary fluid, and the Galerkin method was used to determine the critical Rayleigh numbers for the free-free, rigid-free, and rigid-rigid representing the lower-upper boundaries. The lower and upper boundary was set to be either conducting or insulating to temperature. The purpose of this study is to study the stability of Rayleigh-Benard convection with different temperature conditions in a binary fluid saturated by an anisotropic porous layer. The obtained eigenvalue is numerically solved with respect to various temperatures and velocities using the single-term Galerkin technique. The results, presented graphically, indicate that the rigid-rigid boundaries are more stabilize compared to rigid-free and free-free boundaries. It is also shown that an increase of temperature-dependent viscosity tends to destabilize the onset of double-diffusive convection.

Influence of Rotation and Viscosity on Parallel Rolls of Electrically Conducting Fluid

Rayleigh–Bénard convection is a fundamental fluid dynamics phenomenon that significantly influences heat transfer in various natural and industrial processes, such as geophysical dynamics in the Earth’s liquid core and the performance of heat exchangers. Understanding the behavior of conductive fluids under the influence of heating, rotation, and magnetic fields is critical for improving thermal management systems. Utilizing the Boussinesq approximation, this study theoretically examines the nonlinear convection of a planar layer of conductive liquid that is heated from below and subjected to rotation about a vertical axis in the presence of a magnetic field. We focus on the onset of stationary convection as the temperature difference applied across the planar layer increases. Our theoretical approach investigates the formation of parallel rolls aligned with the magnetic field under free–free boundary conditions. To analyze the system of nonlinear equations, we expand the dependent variables in a series of orthogonal functions and express the coefficients of these functions as power series in a parameter ϵ. A solution for this nonlinear problem is derived through Fourier analysis of perturbations, extending to O(ϵ8), which allows for a detailed visualization of the parallel rolls. Graphical results are presented to explore the dependence of the Nusselt number on the Rayleigh number (R) and Ekman number (E). We observe that both the local Nusselt number and average Nusselt number increase as the Ekman number decreases. Furthermore, the flow appears to become more deformed as E decreases, suggesting an increased influence of external factors such as rotation. This deformation may enhance mixing within the fluid, thereby improving heat transfer between different regions.

Brinkman–Bénard convection in a box with temperature modulation

A bounded porous box saturated with Newtonian fluid and subjected to a sinusoidal temperature gradient has various practical applications, such as solar energy storage, groundwater remediation, food processing, and chemical reactors. We address the generalization of the classical Rayleigh–Bénard convection problem in a horizontal fluid layer in an infinitely large domain heated from below to a finite three-dimensional box. We also look into a more intricate form of the modulated Rayleigh–Bénard problem in which the temperature at the bottom boundary varies sinusoidally. The Rayleigh number quantifies the non-sinusoidal part of the temperature gradient, while the amplitude and frequency of modulation describe the sinusoidal one. The critical Rayleigh number is determined using linear and nonlinear stability analyses; for the latter, the energy method is used. There is a possibility of subcritical instabilities, as evidenced by the energy stability estimates being lower than the linear ones. Furthermore, eigenvalues are obtained as a function of aspect ratios, modulation amplitude, and frequency for varying Darcy numbers. Modulation amplitude more significantly triggers a change in flow patterns at the onset of convection compared to the effect of other parameters. Considering water-saturated porous media made up of different materials, we report the critical temperature difference between lower and upper surfaces required for the onset of convection. In addition, a comparison between such a temperature difference obtained from linear theory and the energy method is also provided in the same manner. It is observed that subharmonic instability occurs for all considered porous media packed densely or sparsely.

Instability of penetrative convection in a vertical porous layer with non-Dirichlet temperature conditions

The linear stability of penetrative convection in a differentially heated vertical porous layer with non-Dirichlet boundary conditions on the perturbed temperature field is investigated. The penetrative convection is realized through a uniform internal heating in a porous medium. The instability-driving parameters are the Darcy-Rayleigh number, dimensionless internal heat source strength, the Prandtl-Darcy number, and the Biot number. Neutral stability curves and the critical values of the Darcy-Rayleigh number, the wave number, and the wave speed are computed numerically by employing the Chebyshev collocation method. A comprehensive analysis is conducted on the onset of thermal instability, focusing on the effects of transitioning temperature boundary conditions from Dirichlet to Neumann. A novel finding is the emergence of bi-modal or tri-modal neutral stability curves, which unveil distinct onset modes arising from the combined effects of a heat source and the transition of boundary conditions from isothermal to adiabatic. The threshold value of the Biot number, at which the transition to instability occurs, shows a significant dependence on the internal heat source strength and this threshold value diminishes as the Prandtl-Darcy number attains higher values. Moreover, increase in the Biot number advances the onset of convection, while the Prandtl-Darcy number is found to exert both stabilizing and destabilizing influences on the stability of the base flow.