Convective State Research Articles

A Non-normal-mode Marginal State of Convection in a Porous Box with Insulating End-Walls

The 4th order Darcy–Benard eigenvalue problem for the onset of thermal convection in a 3D rectangular porous box is investigated. We start from a recent 2D model Tyvand et al. (Transp Porous Med 128:633–651, 2019) for a rectangle with handpicked boundary conditions defying separation of variables so that the eigenfunctions are of non-normal mode type. In this paper, the previous 2D model (Tyvand et al. 2019) is extended to 3D by a Fourier component with wave number k in the horizontal y direction, due to insulating and impermeable sidewalls. As a result, the eigenvalue problem is 2D in the vertical xz-plane, with k as a parameter. The transition from a preferred 2D mode to 3D mode of convection onset is studied with a 2D non-normal mode eigenfunction. We study the 2D eigenfunctions for a unit width in the lateral y direction to compare the four lowest modes $$k_m = m \pi ~(m=0,1,2,3)$$, to see whether the 2D mode $$(m=0)$$ or a 3D mode $$(m\ge 1)$$ is preferred. Further, a continuous spectrum is allowed for the lateral wave number k, searching for the global minimum Rayleigh number at $$k=k_c$$ and the transition between 2D and 3D flow at $$k=k^*$$. Finally, these wave numbers $$k_c$$ and $$k^*$$ are studied as functions of the aspect ratio.

Numerical Study for Darcy–Forchheimer Flow of Nanofluid due to a Rotating Disk with Binary Chemical Reaction and Arrhenius Activation Energy

The present article investigates Darcy–Forchheimer 3D nanoliquid flow because of a rotating disk with Arrhenius activation energy. Flow is created by rotating disk. Impacts of thermophoresis and Brownian dispersion are accounted for. Convective states of thermal and mass transport at surface of a rotating disk are imposed. The nonlinear systems have been deduced by transformation technique. Shooting method is employed to construct the numerical arrangement of subsequent problem. Plots are organized just to investigate how velocities, concentration, and temperature are influenced by distinct emerging flow variables. Surface drag coefficients and local Sherwood and Nusselt numbers are also plotted and discussed. Our results indicate that the temperature and concentration are enhanced for larger values of porosity parameter and Forchheimer number.

Convective boson-fermion pairing mode in one-dimensional oscillating optical superlattice

Boson-fermion mixture exist in nature as quark-gluon plasma and $^3$He-$^4$He mixture. We proposed a convective boson-fermion pairing theory, that can be implemented by ultracold atoms in optical superlattice transformation between different configurations. This transformation may induce the collision and division between boson and fermion, which defines a theoretical convective pairing state. The paring Hamiltonian is Hermitian but it always generate a complex energy spectrum. Each finite gap state can be classified by a topological winding number. The stable pairing state only exists for certain discrete momentum vector zones. An unstable linear dispersion connects two neighboring stable pairing states. The boson-fermion gap function controls the momentum gap space between two neighboring pairing state. The critical temperature of transition from a gapped to gapless phase shows a maximal value at negative fermion chemical potential. The density of state for the pairing excitation diverges at low energy, thus most pairing states are observable at low energy.

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.

Numerical study on the axisymmetric state in spherical Couette flow under unstable thermal stratification

This paper numerically investigates the shear flow between double concentric spherical boundaries rotating differentially, so-called spherical Couette flow, under unstable thermal stratification, focusing on the boundary of the axisymmetric/non-axisymmetric transition in wide gap cases where the inner radius is comparable to the clearance width. While the transition of SCF has been confirmed experimentally in cases without thermal factor, insufficient knowledge on SCF subject to thermal instability, related to geophysical problems especially in wide gap cases, has been accumulated mainly based on numerical analysis; our motivation is to bridge the knowledge gap by a parameter extension. We reconfirm that the transition under no thermal effect is initiated by a disturbance visualised as a spiral pattern with n arms extending from the equatorial zone to the pole in each hemisphere, at the critical Reynolds number, Recr, as previously reported. With increasing thermal factor, the buoyancy effect assists the system rotation to trigger a transition towards non-axisymmetric states, resulting in a relative decrease of Recr. This is in contrast with the result that the system rotation apparently suppresses via Coriolis effect the transition to the thermally convective states at low Reynolds numbers. The present study elucidates that the existence of the axisymmetric state is restricted within a closed area in the extended parameter space, along the boundary of which the spiral patterns observed experimentally in SCF continually connect to the classical spherical Benard convective states.

How organized is deep convection over Germany?

Deep moist convection shows a tendency to organize into mesoscale structures. To be able to understand the potential effect of convective organization on the climate, one needs first to characterize organization. In this study, we systematically characterize the organizational state of convection over Germany based on two years of cloud‐top observations derived from the Meteosat Second Generation satellite and of precipitation cores detected by the German C‐band radar network. The organizational state of convection is characterized by commonly employed organization indices, which are mostly based on the object numbers, sizes and nearest‐neighbour distances. According to the organization index Iorg, cloud tops and precipitation cores are found to be in an organized state for 69% and 92% of the time, respectively. There is an increase in rainfall when the number of objects and their sizes increase, independently of the organizational state. Case‐studies of specific days suggest that convectively organized states correspond to either local multi‐cell clusters, with less numerous, larger objects close to each other, or to scattered clusters, with more numerous, smaller organized objects spread out over the domain. For those days, simulations are performed with the large‐eddy model ICON with grid spacings of 625, 312 and 156 m. Although the model underestimates rainfall and shows a too large cold cloud coverage, the organizational state is reasonably well represented without significant differences between the grid spacings.

Limits on the Extent of the Solsticial Hadley Cell: The Role of Planetary Rotation

Abstract The role of planetary rotation in limiting the extent of the cross-equatorial solsticial Hadley cell (SHC) is investigated using idealized simulations with an aquaplanet general circulation model run under perpetual-solstice conditions. Consistent with previous studies that include a seasonal cycle, the SHC extent increases with decreasing rotation rate, and it occupies the entire globe for sufficiently low planetary rotation rates. A simple theory for the summer-hemisphere extent of the SHC is constructed in which it is assumed that the SHC occupies regions for which a hypothetical radiative–convective equilibrium state is physically unattainable. The theory predicts that the SHC extends farther into the summer hemisphere as the rotation rate is decreased, qualitatively reproducing the behavior of the simulations, but it generally underestimates the simulated SHC extent. A diagnostic theory for the summer-hemisphere SHC extent is then developed based on the assumptions of slantwise convective neutrality and conservation of angular momentum within the Hadley cell. The theory relates the structure of the SHC in the summer hemisphere to the distribution of boundary layer entropy in the dynamically equilibrated simulations. The resultant diagnostic for the SHC extent generalizes the convective quasi-equilibrium-based constraint of Privé and Plumb, in which the position of rain belts is related to maxima in the low-level entropy distribution.

On heat transport and energy partition in thermal convection with mixed boundary conditions

A two-dimensional square enclosure thermally insulated on the vertical walls and heated nonuniformly on the horizontal walls is numerically studied in comparison with the classical Rayleigh-Bénard (RB) convection in the range of Rayleigh number 105 ≤ Ra ≤ 109. Two possible configurations, namely, (1) HCCH and (2) HCHC, are studied in which a unit step function describes the conduction wall temperature as a combination of hot (H) and cold (C) temperatures. The first two letters (of HCCH or HCHC) represent the applied thermal conditions on the bottom wall and the last two letters represent those on the top wall. In the mentioned configurations, the average temperature difference between the bottom and top walls is zero, yet the complex convection state is observed. The diagonally aligned large-scale elliptic roll observed in the RB convection for the Rayleigh number Ra = 108 is found to be replaced by a circular roll in HCCH and a square roll in HCHC. The mean and fluctuating temperature fields in cases of HCCH and HCHC are significantly high as compared to the RB case. We found that heat transport is higher for HCCH and HCHC as compared to the RB convection in a range of 105 ≤ Ra < 108. The increase in heat transport is due to (1) an increase in the background potential energy in the case of HCCH and (2) an increase in the available potential energy in the case of HCHC, which is confirmed by using the global energy budget.

On Moderate-Rayleigh-Number Convection in an Inclined Porous Layer

We investigate the flow structure and dynamics of moderate-Rayleigh-number ( R a ) thermal convection in a two-dimensional inclined porous layer. High-resolution numerical simulations confirm the emergence of O ( 1 ) aspect-ratio large-scale convective rolls, with one ‘natural’ roll rotating in the counterclockwise direction and one ‘antinatural’ roll rotating in the clockwise direction. As the inclination angle ϕ is increased, the background mean shear flow intensifies the natural-roll motion, while suppressing the antinatural-roll motion. Our numerical simulations also reveal—for the first time in single-species porous medium convection—the existence of spatially-localized convective states at large ϕ , which we suggest are enabled by subcritical instability of the base state at sufficiently large inclination angles. To better understand the physics of inclined porous medium convection at different ϕ , we numerically compute steady convective solutions using Newton iteration and then perform secondary stability analysis of these nonlinear states using Floquet theory. Our analysis indicates that the inclination of the porous layer stabilizes the boundary layers of the natural roll, but intensifies the boundary-layer instability of the antinatural roll. These results facilitate physical understanding of the large-scale cellular flows observed in the numerical simulations at different values of ϕ .

Effect of ultrasonic waves on heat transfer in Al2O3 nanofluid under natural convection and pool boiling

Heat transfer in nanofluids due to natural convection and pool boiling (including subcooled boiling and saturated boiling) is analyzed by hot wire method based on the effects of ultrasonic waves in Al2O3 nanofluids. The heat transfer characteristics due to ultrasonic wave propagation in Al2O3 nanofluids under different flow regimes were studied through experiments. In the natural convection state, ultrasonic waves enhance heat transfer in Al2O3 nanofluids, with the highest strengthening heat transfer efficiency reaching 128%. However, the increased heat transfer efficiency showed a downward trend with increased heat flux. Heat transfer in the nanofluid is enhanced by ultrasound when the main body temperature of the fluid is 50 °C, 70 °C and 80 °C under subcooled boiling conditions. However, when the main body temperature is 60 °C, heat transfer in the nanofluid is inhibited by ultrasound, i.e., under saturated boiling condition, ultrasound will still enhance heat transfer in the nanofluids, and the enhanced heat transfer efficiency will decrease with increased heat flux. This paper analyzes experimental results from the aspects of nanoparticle deposition on the heat transfer surface under the influence of ultrasound, the distribution of nanoparticles in liquid, and forces between nanoparticles. In addition, the boiling curves and critical heat flux (CHF) in Al2O3 nanofluids were obtained with and without ultrasound.

Membrane Transport of Nonelectrolyte Solutions in Concentration Polarization Conditions: Hr Form of the Kedem–Katchalsky–Peusner Equations

In this paper, the Kedem–Katchalsky equations in matrix form for nonhomogeneous ternary nonelectrolyte solutions were applied for interpretation of transport through the membrane mounted in horizontal plane. Coefficients Hijr, Hijr, and Hdetr=detHr (for nonhomogeneous solutions), Hij and Hdet=detH (for homogeneous solutions) (i, j ∈ {1, 2, 3}, r = A, B), ψij=HijA−HijB/Hij, and ψdet=HdetA−HdetB/Hdet were calculated on the basis of experimentally determined coefficients (Lp, σ1, σ2ω11, ω22, ω21, ω12, ζ1r, and ζ2r) for glucose in aqueous ethanol solutions and two configurations of the membrane system. From the calculations, it results that the values of coefficients H12r, H13r, H22r, H23r, H32r, H33r, and Hdetr depend nonlinearly on solution concentration as well as on a configuration of membrane system. Besides, the values of coefficients H21r, H12, H21, H22, H33r, and Hdet depend linearly on solution concentration. The value of coefficients H13, H23, and H33 do not depend on solution concentration. The coefficients ψ12, ψ13, ψ22 = ψ23, ψ32 = ψ33, and ψdet depend nonlinearly on solution concentration and for C¯1 ≈ 9.24 mol m−3 are equal to zero. For C¯1 < 9.24 mol m−3, the values of coefficients ψ12 and ψ13 are negative and for C¯1 > 9.23 mol m−3, positive. In contrast, the values of coefficients ψ22 = ψ23, ψ32 = ψ33, and ψdet for C¯1 < 9.24 mol m−3 are positive and for C¯1 > 9.24 mol m−3, negative. For ψ = 0, we can observe nonconvective state, in which concentration Rayleigh number reaches the critical value RC = 1691.09, for ψ<0 is convective state with convection directed straight down and for ψ>0 is convective state with convection directed straight up.

A Non-normal-Mode Marginal State of Convection in a Porous Rectangle

The fourth-order Darcy–Benard eigenvalue problem for onset of thermal convection in a 2D rectangular porous box is investigated. The conventional type of solution has normal-mode dependency in at least one of the two spatial directions. The present eigenfunctions are of non-normal-mode type in both the horizontal and the vertical direction. A numerical solution is found by the finite element method, since no analytical method is known for this non-degenerate fourth-order eigenvalue problem. All four boundaries of the rectangle are impermeable. The thermal conditions are handpicked to be incompatible with normal modes: The lower boundary and the right-hand wall are heat conductors. The upper boundary has given heat flux. The left-hand wall is thermally insulating. The computed eigenfunctions have novel types of complicated cell structures, with intricate internal cell walls.

Numerical study of natural convection in a horizontal concentric annulus using smoothed particle hydrodynamics

Natural convection is of great importance in many engineering applications. This paper presents a smoothed particle hydrodynamics (SPH) method for natural convection simulation. The conservation equations of mass, momentum and energy of fluid are discretized into SPH equations. The body force due to the change of density in a temperature field is considered by the Boussinesq approximation. The SPH method is validated by experimental results in temperature distribution. Then the SPH method is applied to characterize the natural convection in a horizontal cylindrical annulus with varying both Rayleigh number (102 to 107) and Prandtl number (0.01 to 10), while in literature the effect of Prandtl number was usually not considered. In general, the flow is stable at low Rayleigh number but unstable at high Rayleigh number. The numerical results show that the transition Rayleigh number, from stable to unstable, varies with Prandtl number. Four different convection states are identified from numerical simulations, namely, stable state with one plume, unstable state with one plume, stable state with multiple plumes, and unstable state with multiple plumes. The two one-plume states are observed for all Prandtl numbers, while the two multiple-plume states are observed only for Pr = 0.1 and 0.01. It is believed that high thermal diffusivity (low Pr) enhances heat transfer, which modifies the flow and induces instability. An exception case is observed at Pr = 0.1 – the flow is unstable at Ra = 104 but stable at Ra = 105, which can be explained by vortex interactions. Therefore, the flow states depend on not only the Rayleigh and Prandtl numbers but also the vortex interactions.

Inferences from Simple Models of Slow, Convectively Coupled Processes

Abstract A framework for conceptual understanding of slow, convectively coupled disturbances is developed and applied to several canonical tropical problems, including the water vapor content of an atmosphere in radiative–convective equilibrium, the relationship between convective precipitation and column water vapor, Walker-like circulations, self-aggregation of convection, and the Madden–Julian oscillation. The framework is a synthesis of previous work that developed four key approximations: boundary layer energy quasi equilibrium, conservation of free-tropospheric moist and dry static energies, and the weak temperature gradient approximation. It is demonstrated that essential features of slow, convectively coupled processes can be understood without reference to complex turbulent and microphysical processes, even though accounting for such complexity is essential to quantitatively accurate modeling. In particular, we demonstrate that the robust relationship between column water vapor and precipitation observed over tropical oceans does not necessarily imply direct sensitivity of convection to free-tropospheric moisture. We also show that to destabilize the radiative–convective equilibrium state, feedbacks between radiation and clouds and water vapor must be sufficiently strong relative to the gross moist stability.

Pre-mission InSights on the Interior of Mars

Abstract The Interior exploration using Seismic Investigations, Geodesy, and Heat Trans- port (InSight) Mission will focus on Mars’ interior structure and evolution. The basic structure of crust, mantle, and core form soon after accretion. Understanding the early differentiation process on Mars and how it relates to bulk composition is key to improving our understanding of this process on rocky bodies in our solar system, as well as in other solar systems. Current knowledge of differentiation derives largely from the layers observed via seismology on the Moon. However, the Moon’s much smaller diameter make it a poor analog with respect to interior pressure and phase changes. In this paper we review the current knowledge of the thickness of the crust, the diameter and state of the core, seismic attenuation, heat flow, and interior composition. InSight will conduct the first seismic and heat flow measurements of Mars, as well as more precise geodesy. These data reduce uncertainty in crustal thickness, core size and state, heat flow, seismic activity and meteorite impact rates by a factor of 3–10× relative to previous estimates. Based on modeling of seismic wave propagation, we can further constrain interior temperature, composition, and the location of phase changes. By combining heat flow and a well constrained value of crustal thickness, we can estimate the distribution of heat producing elements between the crust and mantle. All of these quantities are key inputs to models of interior convection and thermal evolution that predict the processes that control subsurface temperature, rates of volcanism, plume distribution and stability, and convective state. Collectively these factors offer strong controls on the overall evolution of the geology and habitability of Mars.

Intraseasonal Variability in a Cloud-Permitting Near-Global Equatorial Aquaplanet Model

Abstract Recent studies have suggested that the Madden–Julian oscillation is a result of an instability driven mainly by cloud–radiation feedbacks, similar in character to self-aggregation of convection in nonrotating, cloud-permitting simulations of radiative–convective equilibrium (RCE). Here we bolster that inference by simulating radiative–convective equilibrium states on a rotating sphere with constant sea surface temperature, using the cloud-permitting System for Atmospheric Modeling (SAM) with 20-km grid spacing and extending to walls at 46° latitude in each hemisphere. Mechanism-denial experiments reveal that cloud–radiation interaction is the quintessential driving mechanism of the simulated MJO-like disturbances, but wind-induced surface heat exchange (WISHE) feedbacks are the primary driver of its eastward propagation. WISHE may also explain the faster Kelvin-like modes in the simulations. These conclusions are supported by a linear stability analysis of RCE states on an equatorial beta plane.

Sensitivity of the Amazonian Convective Diurnal Cycle to Its Environment in Observations and Reanalysis

AbstractAtmospheric model parameterizations of tropical deep convection struggle to reproduce the observed diurnal variability of convection in the Amazon leading to climatological biases in the energy budget and water cycle. To identify the physical process contributions to these biases, we analyze the relationships between the convective diurnal cycle and atmosphere state variables relevant to convection in the Amazon using satellite observations and reanalysis data sets for wet and dry seasons between 2002 and 2016 and two Green Ocean Amazon periods. The analysis first stratifies the diurnal cycle into convective and nonconvective days using a daily maximum rain rate threshold of 0.5 mm/hr. Second, the population of days is constrained by requiring reanalysis and observations to agree on the occurrence of convective rain rates, controlling for frequency‐dependent biases in convection. The model‐generated precipitation phase in Modern‐Era Retrospective Analysis for Research and Applications‐2 is closer to observations than ERA during 2002–2016, which exhibits a systematic noontime bias and exaggerated diurnal amplitude. Despite the systematic noontime precipitation bias, ERA produces better agreement with Green Ocean Amazon observations due to the frequent midmorning arrival of the coastal front acting to shift the observed diurnal cycle closer to noon. Model disagreement between middle‐tropospheric vertical velocity is largest overnight during the dissipation stage of convection, acting to sustain biases through radiative effects. Specifically, the slower dissipation of convection in Modern‐Era Retrospective Analysis for Research and Applications‐2 acts to reduce morning surface fluxes and increase convective inhibition, whereas enhanced nocturnal midtropospheric subsidence and higher boundary layer humidity in ERA reduce morning convective inhibition leading to an earlier initiation of afternoon deep convection.

Geomagnetic Dipole Changes and Upwelling/Downwelling at the Top of the Earth's Core

The convective state of the top of Earth's outer core is still under debate. Conflicting evidence from seismology and geomagnetism provides arguments for and against a thick stably stratified layer below the core-mantle boundary. Mineral physics and cooling scenarios of the core favor a stratified layer. However, a non-zero secular variation of the total geomagnetic energy on the core-mantle boundary is evidence for the presence of radial motions extending to the top of the core. We compare the secular variation of the total geomagnetic energy with the secular variation of the geomagnetic dipole intensity and tilt. We demonstrate that both the level of cancellations of the sources and sinks of the dipole intensity secular variation, as well as the level of cancellations of the sources and sinks of the dipole tilt secular variation, are either larger than or comparable to the level of cancellations of the sources and sinks of the total geomagnetic energy secular variation on the core-mantle boundary, indicating that the latter is numerically significant hence upwelling/downwelling reach the top of the core. Radial motions below the core-mantle boundary are either evidence for no stratified layer or to its penetration by various dynamical mechanisms, most notably lateral heterogeneity of core-mantle boundary heat flux.

Numerical simulation of MHD oscillatory mixed convection in CZ crystal growth by Lattice Boltzmann method

A two-dimensional axisymmetric swirling thermal lattice Boltzmann model is presented to study the magnetohydrodynamics (MHD) oscillatory mixed convection in the melt of Czochralski silicon crystal growth in this paper. The governing equations are all solved by lattice Boltzmann method. The D2Q9 model is applied to solve the radial and axial velocities of the melt. Two D2Q5 models are adopted to solve the azimuthal (swirling) velocity and the temperature. The comparison with experiment and finite volume method proves that the presented model can be used as an alternative for simulating the axisymmetric crystal growth. Furthermore, simulations of the melt flow structure and heat transfer under a vertical magnetic field are conducted. And the critical Reynolds numbers Recr, which lead to the onset of the oscillatory melt convection, are calculated in different Richardson numbers (Ri), Ri=0.1,0.5,1.0,1.5,2.0,3.0, and different Hartmann numbers (Ha), Ha=0,10,20,30,40,50. In addition, the magnetic stability diagram is established according to a series of computations and the relationship between crystal rotation parameter and the state of the melt convection are analyzed. Compared with the traditional three-dimensional computational model, the proposed model in this paper has less computation time in simulating the axisymmetric swirling flow without affecting the accuracy of the results. The obtained critical Reynolds number has certain reference for improving the crystal growth parameter in practice.

Linear Stability of Moist Convecting Atmospheres. Part I: From Linear Response Functions to a Simple Model and Applications to Convectively Coupled Waves

Abstract A procedure is presented to systematically construct simple models for the linear stability of moist convecting atmospheres. First, linear response functions of a cumulus ensemble constructed from cloud-system-resolving models are coupled with matrices expressing two-dimensional large-scale linear wave dynamics. For a radiative–convective equilibrium reference state, this model gives two branches of unstable modes: a propagating convectively coupled wave branch and a stationary branch related to storage of column-integrated moist static energy (MSE). The stationary branch is unstable only when radiative feedback is included, while the convectively coupled wave branch is less affected by radiative feedback. With a modular order-reduction procedure from control theory, the linear-response-function-based model is reduced to a system of six ordinary differential equations while still capturing the essential features of the unstable modes (eigenvalues and structures). The six-dimensional system is then split into a slow and a fast manifold. The slow manifold (again, reflecting column MSE storage) is essential for the stationary mode but not for the convectively coupled waves. The fast manifold is then transformed into a form similar to that of prior simple models of convectively coupled waves, thus placing those models and the insights derived from them on a firmer footing. The procedure also better quantifies the parameters of such simple models and allows the stability difference between different reference states to be better understood.