Laminar-Turbulent Bifurcation Scenario in 3D Rayleigh-Benard Convection Problem

We are considering two initial-boundary value problems for Rayleigh-Benard convection in Oberbeck-Boussinesq approximation for incompressible fluid in 3D-rectangular domain with 4:4:1 geometric ratio with periodicity in two directions and cubic domain with 1:1:1 ratio and zero velocity and temperature gradient boundary conditions. For this purpose, we use two numerical method: one is a Pseudo-Spectral-Galerkin method with trigonometric-Chebyshev polynomials and the other is finite element/volume method with WENO interpolation for advection term. Numerical methods are presented shortly and are benchmarked against known DNS data and against one another (for quasi-periodic domain problem). Then we perform stability analysis using analytical expression for main stationary solutions and eigenvalue numerical analysis by applying Implicitly Restarted Arnoldi (IRA) method. The IRA is used to perform linear stability analysis, find bifurcations of stationary points and analyze eigenvalues of monodromy matrices. Thus characteristic exponents of the system for time periodic solutions (limited cycles of various periods and resonance invariant tori) are computed. We show, numerically, the existence of multistable rotes to chaos through chaotic fractal attractors, full Feigenbaum-Sharkovski cascades and multidimensional torus attractors (Landau-Hopf scenario). The existence of these attractors is shown through analysis of phase subspaces projections, Poincare sections and eigenvalue analysis of numerically computed DNS data. These attractors burst into chaos with the increase of Rayleigh number either through resonance and phase-locking or through emergence of singular chaotic attractors.

Effect of Fin Orientation and Length on the Rayleigh-Benard Convection

Natural convection driven by the temperature difference of horizontal top and bottom surfaces of an enclosure containing air, Pr = 0.7, and fins of different arrangements at different lengths is studied numerically for Ra = 105 and 5 × 10^5. Evolution of heat transfer rates （Nusselt number） is illustrated along with various, steady or unsteady, cellular flow structures and temperature patterns. The effect of fin length and placement on flow regime and heat transfer is established. Different fin orientations at the walls are observed to introduce considerable unsteadiness in some cases, requiring close investigation in order to design systems for specific purposes.

Isolated deep convections over the Tibetan Plateau in the rainy season during 2001–2020

The Tibetan Plateau(TP)is a prevalent region for convection systems due to its unique thermodynamic forcing.This study investigated isolated deep convections(IDCs),which have a smaller spatial and temporal size than mesoscale convective systems(MCSs),over the TP in the rainy season(June-September)during 2001–2020.The authors used satellite precipitation and brightness temperature observations from the Global Precipitation Measurement mission.Results show that IDCs mainly concentrate over the southern TP.The IDC number per rainy season decreases from around 140 over the southern TP to around 10 over the northern TP,with an average 54.2.The initiation time of IDCs exhibits an obvious diurnal cycle,with the peak at 1400–1500 LST and the valley at 0900–1000 LST.Most IDCs last less than five hours and more than half appear for only one hour.IDCs generally have a cold cloud area of 7422.9 km^(2),containing a precipitation area of approximately 65%.The larger the IDC,the larger the fraction of intense precipitation it contains.IDCs contribute approximately 20%–30%to total precipitation and approximately 30%–40%to extreme precipitation over the TP,with a larger percentage in July and August than in June and September.In terms of spatial distribution,IDCs contribute more to both total precipitation and extreme precipitation over the TP compared to the surrounding plain regions.IDCs over the TP account for a larger fraction than MCSs,indicating the important role of IDCs over the region.

WAVELET ANALYSIS OF MULTIFRACTAL AND ITS APPLICATION TO PROCESSING TEMPERATURE DATA IN RAYLEIGH-BENARD CONVECTION

Wavelet transform was firstly used to analyze te singularity of a given signal, and then with the method of wavelet transform modulus maximum(WTMM), the characters of fractal set of triadic Cantor was studied. The results show that one can, not only determine the position of singular of signal, but also estimate the Holder exponent h which describes the strength of singularity and other parameters, such as D(h) and τ(q) correctly. Finally, after applying this method to process temperature data in the Rayleigh-Benard convection further, we found that the multifractal hierarchical and multi-scale structure underlying this flow could be entirely revealed from the parameters h, D(h) and τ(q), and the obtained results agree well with the ones determined from the viewpoint of fractal measures.

Flow structures of turbulent Rayleigh-Benard convection in annular cells with aspect ratio one and larger

We present an experimental study of flow structures in turbulent Rayleigh-Bénard convection in annular cells of aspect ratiosΓ=1,2 and 4,and radius ratio 0.5.The convecting fluid is water with Prandtl number Pr=4.3 and 5.3.Rayleigh number Ra ranges 4.8×10^(7)≤Ra≤4.5×10^(10).The dipole state(two-roll flow structure)forΓ=1 and the quadrupole state(fourroll flow structure)forΓ=2 and 4 are found by multi-temperature-probe measurement.Nusselt number Nu is described by a power-law scaling Nu=0.11Ra^(0.31),which is insensitive to the change of flow structures.However,the Reynolds number Re is influenced by increasing aspect ratios,where Re is found to scale with Ra andΓas Re~Ra^(0.46)Γ^(-0.52).The normalized amplitudes of two flow structures as a function of Ra exist difference.Based on relative weights of the first four modes using the Fourier analysis,we find that the first mode dominates inΓ=1 cell,but the second mode contains the most energy inΓ=2 and 4 cells.With increasingΓ,the flow structures exhibit different characteristics.

Convection and Stratification of Temperature and Concentration

This study is devoted to an analysis of natural convection and the emergence of delamination in an incompressible fluid encapsulated in a closed region heated from the side.Weak,medium and intensive modes of stationary laminar thermal and thermo-concentration convection are considered.It is shown that nonlinear flow features can radically change the flow structure and characteristics of heat and mass transfer.Moreover,the temperature and concentration segregation in the center of the square region display a non-monotonic dependence on the Grashof number(flow intensity).The formation of a nonstationary periodic structure of thermal convection in boundary layers and in the core of a convective flow in the closed region is also examined.Details of the formation of countercurrents inside the region with the direction opposite to the main convective flow are given.Finally,the influence of vertical and horizontal vibrations on oscillatory convection is analyzed in detail.

Shallow Convection Dataset Simulated by Three Different Large Eddy Models

Shallow convection plays an important role in transporting heat and moisture from the near-surface to higher altitudes,yet its parameterization in numerical models remains a great challenge,partly due to the lack of high-resolution observations.This study describes a large eddy simulation(LES)dataset for four shallow convection cases that differ primarily in inversion strength,which can be used as a surrogate for real data.To reduce the uncertainty in LES modeling,three different large eddy models were used,including SAM(System for Atmospheric Modeling),WRF(Weather Research and Forecasting model),and UCLA-LES.Results show that the different models generally exhibit similar behavior for each shallow convection case,despite some differences in the details of the convective structure.In addition to grid-averaged fields,conditionally sampled variables,such as in-cloud moisture and vertical velocity,are also provided,which are indispensable for calculation of the entrainment/detrainment rate.Considering the essentiality of the entraining/detraining process in the parameterization of cumulus convection,the dataset presented in this study is potentially useful for validation and improvement of the parameterization of shallow convection.

Numerical Simulation of Thermocapillary Convection with Evaporation Induced by Boundary Heating

The dynamics of a bilayer system filling a rectangular cuvette subjected to external heating is studied.The influence of two types of thermal exposure on the flow pattern and on the dynamic contact angle is analyzed.In particular,the cases of local heating from below and distributed thermal load from the lateral walls are considered.The simulation is carried out within the frame of a two-sided evaporative convection model based on the Boussinesq approximation.A benzine–air system is considered as reference system.The variation in time of the contact angle is described for both heating modes.Under lateral heating,near-wall boundary layers emerge together with strong convection,whereas the local thermal load from the lower wall results in the formation of multicellular motion in the entire volume of the fluids and the appearance of transition regimes followed by a steady-state mode.The results of the present study can aid the design of equipment for thermal coating or drying and the development of methods for the formation of patterns with required structure and morphology.

Libration-Generated Average Convection in a Rotating Flat Layer with Horizontal Axis

The study of average convection in a rotating cavity subjected to modulated rotation is an interesting area for the development of both fundamental and applied science.This phenomenon finds application in the field of mass transfer and fluid flow control,relevant examples being crystal growth under reduced gravity and fluid mixing in microfluidic devices for cell cultures.In this study,the averaged flow generated by the oscillating motion of a fluid in a planar layer rotating about a horizontal axis is experimentally investigated.The boundaries of the layer are maintained at constant temperatures,while the lateral cylindrical wall is thermally insulated.It is demonstrated that libration results in intense oscillatory fluid motion,which in turn produces a time-averaged flow.For the first time,quantitative measures for the instantaneous velocity field are obtained using the Particle Image Velocimetry technique.It is revealed that the flow has the form of counter-rotating vortices.The vortex circulations sense changes during a libration cycle.An increase in the rotation rate and amplitude of the cavity libration results in an increase in the flow intensity.The heat transfer and time-averaged velocity are examined accordingly as a function of the dimensionless oscillation frequency,and resonant excitation of heat transfer and average oscillation velocity are revealed.The threshold curve for the onset of the averaged convection is identified in the plane of control parameters(dimensionless rotational velocity and pulsation Reynolds number).It is found that an increase in the dimensionless rotational velocity has a stabilizing effect on the onset of convection.

Natural Convection of a Power-Law Nanofluid in a Square Cavity with a Vertical Fin

The behavior of non-Newtonian power-law nanofluids under free convection heat transfer conditions in a cooled square enclosure equipped with a heated fin is investigated numerically.In particular,the impact of nanofluids,composed of water and Al_(2)O_(3),TiO_(2),and Cu nanoparticles,on heat transfer enhancement is examined.The aim of this research is also to analyze the influence of different parameters,including the Rayleigh number(Ra=10^(4)-10^(6)),nanoparticle volume fraction(φ=0%-20%),non-Newtonian power-law indexes(n=0.6-1.4),and fin dimensions(Ar=0.3,0.5,and 0.7).Streamlines and isotherms are used to depict flow and related heat transfer characteristics.Results indicate that thermal performance improves with increasing Rayleigh number,regardless of the nanoparticle type or nanofluid rheological behavior.This suggests that the buoyancy force has a significant impact on heat transfer,particularly near the heat source.The Nusselt number is more sensitive to variations in Cu nanoparticle volume fractions compared to Al₂O₃and TiO₂.Moreover,the average Nusselt numbers for power-law nanofluids with n<1(n>1)are greater(smaller)than for Newtonian fluids due to the decrease(increase)in viscosity with increasing(decreasing)shear rate,at the same values of Rayleigh number Ra owing to the amplification(attenuation)of the convective transfer.Notably,the most substantial enhancement is observed with Cu-water shear-thinning nanofluid,where the Nusselt number increases by 136%when changing from Newtonian to shear thinning behavior and by 154.9%when adding 16%nanoparticle volume fraction.Moreover,an even larger increase of 57%in the average Nusselt number is obtained on increasing the fin length from 0.3 to 0.7.

Understanding Simulated Causes of Damaging Surface Winds in a Derecho-Producing Mesoscale Convective System near the East China Coast Based on Convection-Permitting Simulations

A mesoscale convective system(MCS) occurred over the East China coastal provinces and the East China Sea on 30April 2021, producing damaging surface winds near the coastal city Nantong with observed speeds reaching 45 m s^(–1). A simulation using the Weather Research and Forecasting model with a 1.5-km grid spacing generally reproduces the development and subsequent organization of this convective system into an MCS, with an eastward protruding bow segment over the sea. In the simulation, an east-west-oriented high wind swath is generated behind the gust front of the MCS. Descending dry rear-to-front inflows behind the bow and trailing gust front are found to feed the downdrafts in the main precipitation regions. The inflows help to establish spreading cold outflows and enhance the downdrafts through evaporative cooling. Meanwhile, front-to-rear inflows from the south are present, associated with severely rearward-tilted updrafts initially forming over the gust front. Such inflows descend behind(north of) the gust front, significantly enhancing downdrafts and near-surface winds within the cold pool. Consistently, calculated trajectories show that these parcels that contribute to the derecho originate primarily from the region ahead(south) of the east-west-oriented gust front, and dry southwesterly flows in the low-to-middle levels contribute to strong downdrafts within the MCS. Moreover, momentum budget analyses reveal that a large westward-directed horizontal pressure gradient force within the simulated cold pool produced rapid flow acceleration towards Nantong. The analyses enrich the understanding of damaging wind characteristics over coastal East China and will prove helpful to operational forecasters.

Cold filament frontogenesis and frontolysis induced by thermal convection turbulence using large eddy simulation

The frontogenetic processes of a submesoscale cold filament driven by the thermal convection turbulence are studied by a non-hydrostatic large eddy simulation.The results show that the periodic changes in the direction of the cross-filament secondary circulations are induced by the inertial oscillation.The change in the direction of the secondary circulations induces the enhancement and reduction of the horizontal temperature gradient during the former and later inertial period,which indicates that the frontogenetical processes of the cold filament include both of frontogenesis and frontolysis.The structure of the cold filament may be broken and restored by frontogenesis and frontolysis,respectively.The magnitude of the down-filament currents has a periodic variation,while its direction is unchanged with time.The coupling effect of the turbulent mixing and the frontogenesis and frontolysis gradually weakens the temperature gradient of the cold filament with time,which reduces frontogenetical intensity and enlarges the width of cold filament.

Three-Dimensional Convection in an Inclined Porous Layer Subjected to a Vertical Temperature Gradient

In this paper,we study the onset and development of three-dimensional convection in a tilted porous layer saturated with a liquid.The layer is subjected to a gravitational field and a strictly vertical temperature gradient.Typically,problems of thermal convection in tilted porous media saturated with a liquid are studied by assuming constant different temperatures at the boundaries of the layer,which prevent these systems from supporting conductive(non-convective)states.The boundary conditions considered in the present work allow a conductive state and are representative of typical geological applications.In an earlier work,we carried out a linear stability analysis of the conductive state.It was shown that at any layer tilt angles,the most dangerous type of disturbances are longitudinal rolls.Moreover,a non-zero velocity component exists in z-direction.In the present work,threedimensional non-linear convection regimes are studied.The original three-dimensional problem is reduced to two-dimensional one with an analytical expression for the velocity z-component v_(z)=v_(z)(x,y).It is shown that the critical Rayleigh number values obtained through numerical solutions of the obtained 2D problem by a finite difference method for different layer inclination angles,are in a good agreement with those predicted by the linear theory.The number of convective rolls realized in nonlinear calculations also fits the linear theory predictions for a given cavity geometry.Calculations carried out at low supercriticalities show that a direct bifurcation takes place.With increasing supercriticality,no transitions to other convective regimes are detected.The situation studied in this problem can be observed in oil-bearing rock formations under the influence of a geothermal temperature gradient,where the ensuing fluid convection can affect the distribution of oil throughout the layer.

Development of Asymmetric Convection in a Tropical Cyclone under Environmental Uniform Flow and Vertical Wind Shear

Idealized numerical simulations have been carried out to reveal the complexity in the development of asymmetric convection in a tropical cyclone(TC)under the influence of an environment with either uniform flow,vertical wind shear(VWS),or both.Results show that rainwater is enhanced to the right of the motion in the outer rainband,but such enhancement occurs in the upshear-left area of the inner-core region.Additionally,due to the asymmetries introduced by environmental flow,wavenumber-1 temperature and height anomalies develop at a radius of~1000 km in the upper levels.A sub-vortex aside from the TC center encompassing the wavenumber-1 warm center appears,and asymmetric horizontal winds emerge,which,in turn,changes the storm-scale(within 400 km)VWS.Deep convection in the inner core closely follows the changing storm-scale VWS when its magnitude is larger than 2 m s^(-1) and is located downshear of the storm-scale VWS in all the experiments with environmental flow.In the outer rainbands,the maximum boundary layer convergence is mainly controlled by the direction of motion and is located in the rear-right quadrant.These results extend upon the findings of previous studies in three aspects:(1)The discovery of the roughly linear combination effect from the uniform flow and large-scale VWS;(2)The development of upper-level asymmetric winds on a 1000-km scale through the interaction between the TC vortex and environmental flow,resulting in changes in the storm-scale VWS pattern within the TC area;(3)The revelation that TC asymmetric convection closely aligns with the direction-varying storm-scale VWS instead of the initially designated VWS.

On the Features of Thermal Convection in a Compressible Gas

The fully nonlinear equations of gas dynamics are solved in the framework of a numerical approach in order to study the stability of the steady mode of Rayleigh-Bénard convection in compressible,viscous and heat-conducting gases encapsulated in containers with no-slip boundaries and isothermal top and bottom walls.An initial linear temperature profile is assumed.A map of the possible convective modes is presented assuming the height of the region and the value of the temperature gradient as influential parameters.For a relatively small height,isobaric convection is found to take place,which is taken over by an adiabatic mode when the height exceeds the critical value,or by a super-adiabatic mode in case of a relatively high temperature gradient.In the adiabatic mode,convective flow develops due to adiabatic processes given a stable initial stratification.An analytic formula for the critical height of the region is derived taking into account and neglecting the dependence of the gas viscosity on the temperature.Moreover,an analytic formula is obtained for the upper boundary of the region of applicability of the Boussinesq approximation for incompressible gases.These models for compressible gases are relevant to practical situations such as the study of convective flows in spatially extended gas mixtures when dealing with safety issues related to hydrocarbons stored in gas stations.A dangerous situation arises when the tank is almost empty but some hydrocarbon is left at the bottom of the tank.In the presence of convective flows,the vaporized fuel is mixed with the oxidizer(air)forming a gas-vapor medium.However,if the volumetric concentration of fuel vapor(hydrocarbon)is in the interval between the lower and upper concentration limits of ignition,then the gas-vapor mixture becomes explosive and any accidental spark is sufficient to cause an emergency.

Updated Lagrangian Particle Hydrodynamics (ULPH)Modeling of Natural Convection Problems

Natural convection is a heat transfer mechanism driven by temperature or density differences,leading to fluid motion without external influence.It occurs in various natural and engineering phenomena,influencing heat transfer,climate,and fluid mixing in industrial processes.This work aims to use the Updated Lagrangian Particle Hydrodynamics(ULPH)theory to address natural convection problems.The Navier-Stokes equation is discretized using second-order nonlocal differential operators,allowing a direct solution of the Laplace operator for temperature in the energy equation.Various numerical simulations,including cases such as natural convection in square cavities and two concentric cylinders,were conducted to validate the reliability of the model.The results demonstrate that the proposed model exhibits excellent accuracy and performance,providing a promising and effective numerical approach for natural convection problems.

Finite Element Analysis for Magneto-Convection Heat Transfer Performance in Vertical Wavy Surface Enclosure:Fin Size Impact

The goal of this paper is to represent a numerical study of magnetohydrodynamic mixed convection heat transfer in a lid-driven vertical wavy enclosure with a fin attached to the bottomwall.We use a finite elementmethod based on Galerkin weighted residual(GWR)techniques to set up the appropriate governing equations for the present flow model.We have conducted a parametric investigation to examine the impact of Hartmann and Richardson numbers on the flow pattern and heat transmission features inside a wavy cavity.We graphically represent the numerical results,such as isotherms,streamlines,velocity profiles,local and mean Nusselt numbers,and average surface temperature.Comparisons between the results of this work and previously published work in a literature review have been produced to examine the reliability and consistency of the data.The different sizes of the fin surface significantly impact flow creation and temperature fields.Additionally,the long fin size is necessary to enhance the heat transfer rate on the right surface at large Richardson numbers and low Hartmann numbers.Fin surfaces can significantly increase the mixing of fluid inside the enclosure,which can mean reductions in reaction times and operating costs,along with increases in heat transfer and efficiency.

Mechanism of Thermally Radiative Prandtl Nanofluids and Double-Diffusive Convection in Tapered Channel on Peristaltic Flow with Viscous Dissipation and Induced Magnetic Field

The application of mathematical modeling to biological fluids is of utmost importance, as it has diverse applicationsin medicine. The peristaltic mechanism plays a crucial role in understanding numerous biological flows. In thispaper, we present a theoretical investigation of the double diffusion convection in the peristaltic transport of aPrandtl nanofluid through an asymmetric tapered channel under the combined action of thermal radiation andan induced magnetic field. The equations for the current flow scenario are developed, incorporating relevantassumptions, and considering the effect of viscous dissipation. The impact of thermal radiation and doublediffusion on public health is of particular interest. For instance, infrared radiation techniques have been used totreat various skin-related diseases and can also be employed as a measure of thermotherapy for some bones toenhance blood circulation, with radiation increasing blood flow by approximately 80%. To solve the governingequations, we employ a numerical method with the aid of symbolic software such as Mathematica and MATLAB.The velocity, magnetic force function, pressure rise, temperature, solute (species) concentration, and nanoparticlevolume fraction profiles are analytically derived and graphically displayed. The results outcomes are compared withthe findings of limiting situations for verification.

Absolute scaling law for temperature data in Rayleigh-Benard convection

In addition to the hierarchical-structure (H-S) model, this paper further explores the most intensive intermittent structure of Rayleigh-Bénard convection at the high Ra numbers proportional to temperature. With respect to the discovery and by means of the scale, both of Bolgiano, there are two regions of the structure holding the absolute scaling law given by Ching’s paper. Through theoretic analysis of data, this paper indicates that the regions act as two local intensive intermittent structures, by which the statistical absolute scaling performance of region is induced, rather than the statistical result of the entire time series in belief since 1941. In terms of statistical theory, the local structure in fluid, therefore, is the essence governing the absolute scaling performance of region, especially in high intensity.

Numerical Predictions of Laminar Forced Convection Heat Transfer with and without Buoyancy Effects from an Isothermal Horizontal Flat Plate to Supercritical Nitrogen

Numerical predictions are made for Laminar Forced convection heat transfer with and without buoyancy effects for Supercritical Nitrogen flowing over an isothermal horizontal flat plate with a heated surface facing downwards.Computations are performed by varying the value ofΔT from5 to 30 K and P_(∞)/P_(cr)ratio from1.1 to 1.5.Variation of all the thermophysical properties of supercritical Nitrogen is considered.The wall temperatures are chosen in such a way that two values of Tw are less than T∗(T*is the temperature at which the fluid has a maximum value of Cp for the given pressure),one value equal to T∗and two values greater than T∗.Three different values of U∞are used to obtain Re∞range of 3.6×10_(4)to 4.74×10^(5)for forced convection without buoyancy effects and Gr_(∞)/Re^(2)_(∞)range of 0.011 to 3.107 for the case where buoyancy effects are predominant.Six different forms of correlations are proposed based on numerical predictions and are compared with actual numerical predictions.It has been found that in all six forms of correlations,the maximum deviations are found to occur in those cases where the pseudocritical temperature TT∗lies between the wall temperature and bulk fluid temperature.