Oscillatory Convection Research Articles

Effect of side wall conditions and aspect ratio on convective pattern formation in Rayleigh-Benard convection

Effect of side wall boundary conditions and aspect ratio in very small boxes on patterns formed during Raleigh-Benard (RB) convection is studied using an indigenously developed flow solver based on the finite difference method. While keeping the bottom (hot) and top (cold) walls isothermal, the side wall thermal conditions are kept either constant heat flux or isothermal type. For constant heat flux side wall condition, the considered value of heat flux lies between 0 and maximum corresponding to conductive heat flux between top and bottom walls. For isothermal side wall condition, the chosen value of temperature is between the top and bottom wall temperatures. The computational domain is a cube or a square prism with aspect ratio in longitudinal direction (ARx) varied between 1.2 and 2 in steps of 0.2. For fixed value of ARx = 1.6, aspect ratio in transverse direction (ARz) has been varied for adiabatic side wall conditions. Effect of side wall condition on orientation of roll axis and the number of rolls has been investigated with observations well supported by stream traces and temperature contours. Moreover, for selected parameters, based on nature of pattern formation for steady flow, onset of oscillatory convection is explained.

Intraseasonal Convection and Air–Sea Fluxes Over the Indian Monsoon Region Revealed from the Bimodal ISO Index

The present study aims to elucidate the intraseasonal oscillations (ISO) of atmospheric convection and air–sea fluxes over the Indian region during summer monsoon season. To accomplish this, the study employs the extended empirical orthogonal function-based bimodal ISO index developed by Kikuchi et al. [Clim Dyn 38(9–10):1989–2000, 2012]. The propagation of deep convective anomalies and air–sea fluxes are explored during the different phases (P1–P8) of the bimodal index. This is achieved by examining the Tropical Rainfall Measuring Mission satellite rainfall, outgoing long-wave radiation (OLR), sea surface temperatures (SST), downward shortwave radiation (DSR) and reanalysis products of 850-hPa winds, potential vorticity and latent heat fluxes (LHFs). Composite analysis of the anomalies depicts the strong (weak) northward (eastward) propagation of convective anomalies over the Indian region (equatorial Indian Ocean). Over the Indian region, active (suppressed or weak) convection is evident during the phases of P4 and P5 (P1, P2 and P7, P8). Enhanced deep convection is lead by a phase of 850-hPa westerly winds and negative SST anomalies. Signatures of ISO during different phases are examined from Research Moored Array for African-Asian-Australian Monson Analysis and Prediction (RAMA) buoy observations over the Bay of Bengal. Rainfall, SST and LHF anomalies from RAMA buoy measurements are in concurrence with the spatial composites of bimodal ISO phases. Plausible drivers for the variability of intraseasonal convection and air–sea fluxes were reviewed using published observational and modelling studies. Findings from the present study advocate the applicability of Kikuchi bimodal index [Clim Dyn 38(9–10):1989–2000, 2012] over the Indian region and have practical application for the validation of ocean-atmospheric coupled models.

Oscillatory flows of electro-thermo-convection in eccentric annulus

A detailed numerical investigation for oscillatory electro-thermo-convection of dielectric liquids in horizontal eccentric annulus is carried out based on a unified lattice Boltzmann method (LBM). The liquid is under the simultaneous action of a strong unipolar charge injection and a thermal gradient. The self-oscillatory behaviors and heat transfer characteristics for different Rayleigh number Ra, electric Rayleigh number T, Prandtl number Pr, mobility parameter M and radii ratio are studied systematically. The results show that the values of Ra within the range from 103 to 104 have little effect on the periodic oscillatory convection, while the flow develops from steady to periodic oscillatory and finally evolves into chaotic as T increases, and the fundamental frequency and the fluctuation amplitude as well as the heat transfer rate increase with T. Moreover, it is found that the fluid properties have significant impact on the oscillatory convection, and the formation of oscillating flows is strongly related to the value of radius ratio.

Laser-Induced Superintensive Bubble Boiling

Superintensive bubble boiling (SBB) is implemented in water in the absence of degassing at the end surface of a laser fiber using 100-ns laser pulses. A thulium fiber laser with a radiation wavelength of 1.94 μm and moderate power is used as a radiation source. The generation of bubble microjets in the vicinity of the end surface of the laser fiber is studied with the aid of high-speed photography and acoustic methods. After a threshold transition to the SBB regime, the energy of acoustic emission is predominantly concentrated in an acoustic interval of 10–30 kHz. The acoustic signal is generated due to thermal cavitation. Record-high thermal fluxes of up to 0.16 MW/cm2 are reached in the SBB regime. Parameters of the resulting convective fluxes, microbubbles, and broadband acoustic oscillations are determined.

Linear and nonlinear stability of Soret‐Dufour Lapwood convection near double codimension‐2 points

AbstractIn this study, the Dufour and Soret effects on natural double‐diffusion convection in a horizontal porous layer was studied numerically using FORTRAN 90 programming and analytically near various convection onset thresholds. The porous layer was subject to a uniform heat and mass fluxes on the horizontal walls while the vertical walls were impermeable and adiabatic. The Darcy model along with the Boussinesq approximation was assumed in the problem formulation. The governing parameters of the problem are the thermal Rayleigh number, RT, the buoyancy ratio, N, the Lewis number, Le, the aspect ratio of the cavity, A, and the Dufour, Du, and Soret, Sr, numbers. For a shallow enclosure, the analytical solution was derived assuming zero convection wave number, which is valid near and above criticality. The onset of subcritical, supercritical and oscillatory convection was investigated. Two linear and nonlinear codimension‐2 points were found to exist. Whether the system was subject to constant fluxes and heat and solute, regardless of the aspect ratio of the layer, the subcritical convection behavior remained the same with similarity in the thresholds expressions for subcritical bifurcation.

Double-diffusive instabilities at a horizontal boundary after the sudden onset of heating

When a deep body of fluid with a stable salinity gradient is heated from below at a horizontal boundary a destabilizing temperature gradient develops and can lead to instabilities. We will focus on two variants of this problem: the sudden increase in the boundary temperature at the initial time and the sudden turning on of a constant heat flux. These generate time-dependent temperature profiles. We look at the growing phase of the linear instabilities as an initial value problem where the initial time for the instabilities is a parameter to be determined. We determine numerically the optimal initial conditions and the optimal starting time for the instabilities to ensure that the maximum growth occurs at some given later time. The method that is used is an extension of the method developed by Kerr & Gumm (J. Fluid Mech., vol. 825, 2017, pp. 1002–1034) in their investigation of the stability of developing temperature boundary layers at horizontal and vertical boundaries. This requires the use of an appropriate measure of the amplitude of the disturbances which is identified. The effectiveness of this approach is verified by looking at the classic problem of double-diffusive convection in a horizontal layer, where we look at both the salt-finger regime and the diffusive regime. We show that this approach is an effective way of investigating instabilities where the background gradients time dependent. For the problem of heating a salinity gradient from below, as the heat diffuses into the fluid the effective thermal Rayleigh number based on the instantaneous diffusion length scale grows. For the case of a sudden increase in the temperature by a fixed amount the effective thermal Rayleigh number is proportional to $t^{3/2}$, and for a constant heat flux it is proportional to $t^{2}$, where $t$ is the time since the onset of heating. However, the effective salt Rayleigh number also grows as $t^{2}$. We will show that for the constant temperature case the thermal Rayleigh number initially dominates and the instabilities undergo a phase where the convection is essentially thermal, and the onset is essentially instantaneous. As the salt Rayleigh number becomes more significant the instability undergoes a transition to oscillatory double-diffusive convection. For the constant heat flux the ratio of the thermal and salt Rayleigh numbers is constant, and the instabilities are always double diffusive in their nature. These instabilities initially decay. Hence, to achieve the largest growth at some given fixed time, there is an optimal time after the onset of heating for the instabilities to be initiated. These instabilities are essentially double diffusive throughout their growth.

GONG p-Mode Parameters Through Two Solar Cycles

We investigate the parameters of global solar p-mode oscillations, namely damping width Gamma, amplitude A, mean squared velocity langle v^{2}rangle, energy E, and energy supply rate mathrm{d}E/mathrm{d}t, derived from two solar cycles’ worth (1996 – 2018) of Global Oscillation Network Group (GONG) time series for harmonic degrees l=0,mbox{--},150. We correct for the effect of fill factor, apparent solar radius, and spurious jumps in the mode amplitudes. We find that the amplitude of the activity-related changes of Gamma and A depends on both frequency and harmonic degree of the modes, with the largest variations of Gamma for modes with 2400~upmumbox{Hz}lenule3300~upmumbox{Hz} and 31le l le60 with a minimum-to-maximum variation of 26.6pm0.3% and of A for modes with 2400~upmumbox{Hz}lenule 3300~upmumbox{Hz} and 61le l le100 with a minimum-to-maximum variation of 27.4pm0.4%. The level of correlation between the solar radio flux F_{10.7} and mode parameters also depends on mode frequency and harmonic degree. As a function of mode frequency, the mode amplitudes are found to follow an asymmetric Voigt profile with nu_{text{max}}=3073.59pm0.18~upmumbox{Hz}. From the mode parameters, we calculate physical mode quantities and average them over specific mode frequency ranges. In this way, we find that the mean squared velocities langle v^{2}rangle and energies E of p modes are anticorrelated with the level of activity, varying by 14.7pm0.3% and 18.4pm0.3%, respectively, and that the mode energy supply rates show no significant correlation with activity. With this study we expand previously published results on the temporal variation of solar p-mode parameters. Our results will be helpful to future studies of the excitation and damping of p modes, i.e., the interplay between convection, magnetic field, and resonant acoustic oscillations.

Double-diffusive Soret convection phenomenon in porous media: effect of Vadasz inertia term

The onset of double-diffusive convection in horizontal porous layers for the thermo-diffusive Soret phenomenon in the case of a generalized Darcy model including inertia term is investigated. Via a linearization principle recently introduced in Rionero (Atti Accad Naz Lincei Rend Cl Sci Fis Mat Natur 28:21–47, 2017) the coincidence between linear and nonlinear (global) stability thresholds of the thermo-solutal conduction solution, is proved. Necessary and sufficient conditions guaranteeing the onset of steady or oscillatory convection in a closed algebraic form are obtained.

Numerical Simulation of Oscillatory MHD Natural Convection in Cylindrical Annulus: Prandtl Number Effect

The oscillatory natural convection between two concentric cylinders is numerically investigated. The effect of Prandtl number on flow and heat transfer characteristics with considering the magnetic field effects is investigated. For different values of physical parameters, critical Rayleigh numbers are determined. For buoyancy term, the Boussinesq approximation is used, and the numerical solutions are obtained using the finite volume method. For this kind of Prandtl number, the flow and heat transfer characteristics are unique and independent of the Prandtl number. Stability diagram (RaCr-Pr) highlights the dependence of RaCr via Prandtl numbers and various Hartmann number. The importance of this modeling is its practical application for stabilizing or weakening the convective effects in the design of magnetic systems.

Thermal Instability Analysis of an Elastico-Viscous Nanofluid Layer

The purpose of this paper is to study the thermal instability analysis of an elastico-viscous nanofluid layer heated from below. The Rivlin-Ericksen type fluid model is used to describe the rheological behavior of an elastico-viscous nanofluid. The linear stability criterion for the onset of both stationary and oscillatory convection is derived by applying the normal model analysis method. The presence of nanoparticles enhances the thermal conductivity of the fluid, and the model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The effect of the physical parameters of the system, namely the concentration Rayleigh number, Prandtl number, capacity ratio, Lewis number, and kinematic visco-elasticity coefficient, on the stability of the system is numerically investigated. In addition, sufficient conditions for the non-existence of oscillatory convection are reported.

Study of a periodically forced magnetohydrodynamic system using Floquet analysis and nonlinear Galerkin modelling

We present a detailed study of Rayleigh–Benard magnetoconvection with periodic gravity modulation and uniform vertical magnetic field. Linear stability analysis is carried out using Floquet theory to construct the stability boundaries in order to estimate the magnitude of forcing amplitude $$\epsilon $$ required for having convection in the system for a fixed Rayleigh number Ra, wave number k and modulating frequency $$\Omega $$ . The effects of varying Prandtl number Pr and Chandrasekhar number Q on the threshold of convection are also investigated. A higher Pr value reduces the value of the threshold, whereas a higher Q value increases it. Bicritical states are also observed at which the minimum forcing amplitude needed for convection to begin occurs at two different k values in harmonic and sub-harmonic regions, respectively. We also construct a nonlinear Galerkin model and compare the results with those obtained from linear stability analysis. Two-dimensional (2D) oscillatory convection is observed at the onset, while quasiperiodic and chaotic behaviours are found at higher Ra values. 2D as well as nonlinear convective flow patterns are observed for primary and higher-order instabilities, respectively. Bifurcation diagrams with respect to different parameters such as $$\epsilon $$ , Ra and Q are provided for thorough understanding of the forced nonlinear system.

Surface tension convection caused by free surface deformation in KTa1−xNbxO3 melts

Experiments on surface tension driven convection of high temperature potassium tantalate niobate (KTa1−xNbxO3, KTN) melts have been carried out in an in-situ observation system. There is a double loop axially symmetric vortex pattern. With the temperature increases, the convection can be transferred from one stable state to oscillatory state and then to another stable state. The oscillatory surface tension convection, which is related to the free surface deformation, can be characterized by the oscillatory main trunk and two unequal branches. The branches depress the large pressure gradient and compensate the return flow to stabilize the circular current. There is a linear decreasing relationship between the deformation angle θ and the oscillatory frequency f. For KTN melts with higher Nb content, the convective pattern is not various, but a smaller degree of deformation can occur accompanied by a weaker oscillation process. The values of critical deformation coefficient S parameter for both the onset and the offset of oscillations decrease with the increase of the content of Nb. The critical values of oscillation satisfy with Son · x ≈ 2.3 × 10−3 and Soff · x ≈ 4.0 × 10−3, respectively.

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.

Oscillatory instability in a reaction front separating fluids of different densities.

Reaction fronts described by the Kuramoto-Sivashinsky (KS) equation can exhibit complex behavior as they separate reacted from unreacted fluids. If the fluid of higher density is above a fluid of lower density, then the Rayleigh-Taylor instability can lead to fluid motion. In the reverse situation, where the lighter fluid is on top, gravitationally driven forces can stabilize a convectionless flat front inhibiting the complex front propagation described by the KS equation. In these cases, a critical density difference is required to provide stability to the flat front. A linear stability analysis shows that the transition from stable to unstable flat fronts can be oscillatory for viscous fluid motion. Once the transition takes place, the fronts exhibit oscillatory convection resulting in oscillations of the shape and speed of the front.

Stability of triple diffusive convection in a viscoelastic fluid-saturated porous layer

The triple diffusive convection in an Oldroyd-B fluid-saturated porous layer is investigated by performing linear and weakly nonlinear stability analyses. The condition for the onset of stationary and oscillatory is derived analytically. Contrary to the observed phenomenon in Newtonian fluids, the presence of viscoelasticity of the fluid is to degenerate the quasiperiodic bifurcation from the steady quiescent state. Under certain conditions, it is found that disconnected closed convex oscillatory neutral curves occur, indicating the requirement of three critical values of the thermal Darcy-Rayleigh number to identify the linear instability criteria instead of the usual single value, which is a novel result enunciated from the present study for an Oldroyd-B fluid saturating a porous medium. The similarities and differences of linear instability characteristics of Oldroyd-B, Maxwell, and Newtonian fluids are also highlighted. The stability of oscillatory finite amplitude convection is discussed by deriving a cubic Landau equation, and the convective heat and mass transfer are analyzed for different values of physical parameters.

Weakly Nonlinear Oscillatory Convection in a Viscoelastic Fluid Saturated Porous Medium with Throughflow and Temperature Modulation

The effect of vertical throughfow and temperature modulation on a viscoelastic fluid saturated porous medium has been investigated. The amplitudes of temperature modulation at the lower and upper surfaces are considered to be very small and the disturbances are expanded in terms of power series of amplitude of convection. A weak nonlinear stability analysis has been performed for the oscillatory mode of convection, and heat transport in terms of the Nusselt number, which is governed by the non autonomous complex Ginzburg- Landau equation, is calculated. The effect of vertical through flow is found to stabilize the system irrespective of the direction of through flow in the case of permeable boundary conditions. The time relaxation has a destabilizing effect, while the time retardation parameter has a stabilizing effect on the system. The effects of amplitude and frequency of modulation on heat transport have been analyzed and depicted graphically. The study shows that the heat transport can be controlled effectively by a mechanism that is external to the system. Further, it is also found that heat transfer is more in oscillatory mode of convection rather than in stationary mode of convection.

Oscillatory natural convection of water‐glycerin mixture in a tall rectangular cavity: Transition to the chaos

AbstractThis paper presents results of a numerical investigation involving bifurcation sequence leading to chaos in natural convection inside a vertically tall rectangular cavity having an aspect ratio equal to 15 and a Prandtl number equal to 125, corresponding to water‐glycerin mixture. The flow is characterized by a vertical stratification of the temperature field for Grashof numbers greater than or equal to 200 that is outside the conduction regime and it is stationary monocellular up to a critical value Grc = 2800 where a periodic oscillatory regime appears. As Grashof number is increased, a transition from a steady periodic bicellular flow to an oscillatory multicellular flow, with 2 main central cells and 2 secondary cells, occurs. The regime remains periodic until Gr = 3100 where there is a first appearance of the chaotic regime which extends over a narrow interval of the Grashof number delimited by Gr = 3200.

Transition from Steady to Oscillatory Flow Natural Convection of Low-Pr Fluids in 3D Bridgman Configuration for Crystal Growth

Transition from Steady to Oscillatory Flow Natural Convection of Low-Pr Fluids in 3D Bridgman Configuration for Crystal Growth

Nonlinear convection of binary liquids in a porous medium.

Thermal convection of binary mixtures in a porous medium is studied with stress-free boundary conditions. The linear stability analysis is studied by using the normal mode method. The effects of the material parameters have been studied at the onset of convection. Using a multiple scale analysis near the onset of the stationary convection, a cubic-quintic amplitude equation is derived. The influence of the Lewis number and the separation ratio on the supercritical-subcritical transition is discussed. Stationary front solutions and localized states are analyzed at the Maxwell point. Near the threshold of the oscillatory convection, a set of two coupled complex cubic-quintic Ginzburg-Landau type amplitude equations is derived, and implicit analytical expressions for the coefficients are given.

Interhemispheric influence of Indo-Pacific convection oscillation on Southern Hemisphere rainfall through southward propagation of Rossby waves

Tropical Indo-western Pacific convection anomalies influence atmospheric circulation, impacting climate far beyond the tropics. Here we present observational and modelling evidence for an interhemispheric effect of the boreal summer (June–August) Indo-Pacific convection oscillation (IPCO), which is characterized by a zonal seesaw pattern between the north Indian Ocean (NIO) and the western North Pacific (WNP). It is found that the IPCO is significantly correlated with simultaneous rainfall over many parts of the Southern Hemisphere (SH), including western Australia and western Brazil. These interhemispheric connections in rainfall remain significant when then El Nino–Southern Oscillation, the Indian Ocean Dipole, and the SH Annular Mode related signals are excluded simultaneously, which may help to improve the SH seasonal predictions. The physical mechanism that underlies this interhemispheric connection is investigated using observations, Rossby wave diagnostics and a series of atmospheric model experiments. Results suggest that convective heating anomalies associated with the IPCO excite two distinct southward-propagating equivalent barotropic wave trains that propagate into the extratropics in the SH: the South Africa–mid-latitudes wave train excited by the heat sink over the NIO, and the Maritime Continent–subtropical Australia wave train excited by the heat source over the WNP. We further demonstrate that upper tropospheric northerlies over tropical Africa and the Indian Ocean are responsible for the southward propagation of stationary Rossby waves across the easterlies. These equivalent barotropic waves then modulate the moisture transport, baroclinicity, and mid-latitude storminess, and thus affect rainfall anomalies in the SH. The new wave train patterns provide novel insight into the teleconnection pathways of convective heating over the tropical Indian Ocean and western Pacific.