Differentially-heated Cavity Research Articles

Non-intrusive diagnostics of differentially-heated two-component immiscible fluid layer with phase change

Experiments on buoyancy-driven convective phenomena in a differentially-heated two component immiscible fluid layer with phase change phenomena have been reported. The real-time mapping of the transients associated with the process has been affected in a complete non-intrusive manner using rainbow schlieren deflectometry. Experiments have been performed for varying heat flux levels supplied to the lower horizontal surface of the cavity and for different heights of the secondary fluid layer. The two-component immiscible fluid mixture comprises of water as the (lighter) primary fluid layer and dichloromethane (DCM) as the (heavier) secondary fluid component. The supplied heat flux levels are sufficient enough to induce phase change in the secondary fluid layer through nucleate pool boiling. In addition to the real-time mapping of the buoyancy-induced convection in both the fluid layers, the process of vapor bubble inception, their growth and departure from the lower heated wall of the cavity have been recorded in the form of time-lapsed schlieren images. Conditions under which the continued interaction of the vapor phase of DCM with the interface leads to interface deformation and its final breakage have been investigated. Based on the force balance analysis, the critical volume of the DCM vapor phase required for interface breakage has been determined. Dependence of parameters such as neck breakage height, time required for interface breakage etc. on the supplied heat flux level and height of the secondary fluid has been investigated. The experimental observations revealed the importance of vapor bubbles-induced fluid agitation in the otherwise stagnant primary fluid layer, disruption of the thermal boundary layer in a completely passive manner as the upward rising vapor volume condenses at the top horizontal surface of the differentially-heated cavity and their implications in possible heat transfer enhancement.

Monolithic projection-based method with staggered time discretization for solving non-Oberbeck–Boussinesq natural convection flows

This paper presents an efficient monolithic projection-based method with staggered time discretization (MPM-STD) to examine the non-Oberbeck–Boussinesq (NOB) effects in several natural convection problems involving dramatic temperature-dependent changes in fluid properties. The proposed approach employs the Crank–Nicolson scheme along with staggered time discretization to discretize the momentum and energy equations. The momentum and energy equations are decoupled by evaluating the velocity vector at integral time levels (n+1), and the scalar variables (pressure and temperature) at half-integral time levels (n+12). The observed density variations in all terms result in a variable-coefficient Poisson equation, which is difficult to solve efficiently. The convergence is accelerated via adoption of an appropriate pressure-correction scheme that transforms the aforementioned Poisson equation to a constant-coefficient form. The numerical simulations concerning two-dimensional (2D) periodic NOB Rayleigh–Bénard convection (RBC) in glycerol and 2D differentially heated cavity (DHC) problem in air confirmed the second-order temporal and spatial accuracies of the proposed method. By simulating the 2D DHC problem in air and the RBC problem in liquid (water or glycerol) considering NOB effects, it is concluded that the proposed MPM-STD significantly mitigates the time-step restriction, thereby increasing the computational efficiency, which exceeds that of existing semi-implicit and explicit schemes. Moreover, the potential of the proposed approach with regard to solving challenging three-dimensional (3D) turbulent problems is demonstrated by performing direct simulations of turbulent RBCs under NOB effects involving temperature differences up to 60 K with a corresponding Rayleigh number (Ra=106).

Numerical Analysis of Algebraic Flux Model using OpenFOAM in Differentially-heated Cavity Configurations

The analysis of the turbulent natural convection is mathematically described by the equations of conservation of mass, energy and momentum. Closing these equations requires modeling turbulent momentum stress and turbulent heat flux using the k-omega Shear Stress Transport Model and Algebraic Flux Model (AFM), respectively. The Reynolds Averaged Navier-Stokes (RANS) methodological setup for an incompressible buoyancy-driven flow has a great potential in modeling the oxide layer of corium for the improvement of in-vessel melt retention-severe accident management guidelines (IVR-SAMG). However, the procedure also requires validation study from experimental data that also exhibit similar flow and thermal behavior. This paper presents the modeling of natural convection in a differentially-heated cavity configuration using standard turbulent heat flux approaches and modified AFM versions using OpenFOAM – an open-source C++-based software. Results showed an improvement of near-wall behavior with up to the thermal boundary thickness of 0.2 m from the heated wall by using AFM as compared with other approaches. Also, sensitivity analysis at varying coefficients in AFM was performed to assess its contribution to heat and fluid phenomena. It was demonstrated that the production term due to the non-uniformity of mean thermal field was highly sensitive up to a factor of 0.60 for buoyant and stratified conditions when AFM was incorporated in RANS approach.

Computational Performance of Disparate Lattice Boltzmann Scenarios under Unsteady Thermal Convection Flow and Heat Transfer Simulation

The present work highlights the capacity of disparate lattice Boltzmann strategies in simulating natural convection and heat transfer phenomena during the unsteady period of the flow. Within the framework of Bhatnagar-Gross-Krook collision operator, diverse lattice Boltzmann schemes emerged from two different embodiments of discrete Boltzmann expression and three distinct forcing models. Subsequently, computational performance of disparate lattice Boltzmann strategies was tested upon two different thermo-hydrodynamics configurations, namely the natural convection in a differentially-heated cavity and the Rayleigh-Bènard convection. For the purposes of exhibition and validation, the steady-state conditions of both physical systems were compared with the established numerical results from the classical computational techniques. Excellent agreements were observed for both thermo-hydrodynamics cases. Numerical results of both physical systems demonstrate the existence of considerable discrepancy in the computational characteristics of different lattice Boltzmann strategies during the unsteady period of the simulation. The corresponding disparity diminished gradually as the simulation proceeded towards a steady-state condition, where the computational profiles became almost equivalent. Variation in the discrete lattice Boltzmann expressions was identified as the primary factor that engenders the prevailed heterogeneity in the computational behaviour. Meanwhile, the contribution of distinct forcing models to the emergence of such diversity was found to be inconsequential. The findings of the present study contribute to the ventures to alleviate contemporary issues regarding proper selection of lattice Boltzmann schemes in modelling fluid flow and heat transfer phenomena.

Towards Uncertainty Quantification of LES and URANS for the Buoyancy-Driven Mixing Process between Two Miscible Fluids—Differentially Heated Cavity of Aspect Ratio 4

Numerical simulations are subject to uncertainties due to the imprecise knowledge of physical properties, model parameters, as well as initial and boundary conditions. The assessment of these uncertainties is required for some applications. In the field of Computational Fluid Dynamics (CFD), the reliable prediction of hydrogen distribution and pressure build-up in nuclear reactor containment after a severe reactor accident is a representative application where the assessment of these uncertainties is of essential importance. The inital and boundary conditions that significantly influence the present buoyancy-driven flow are subject to uncertainties. Therefore, the aim is to investigate the propagation of uncertainties in input parameters to the results variables. As a basis for the examination of a representative reactor test containment, the investigations are initially carried out using the Differentially Heated Cavity (DHC) of aspect ratio 4 with Ra=2×109 as a test case from the literature. This allows for gradual method development for guidelines to quantify the uncertainty of natural convection flows in large-scale industrial applications. A dual approach is applied, in which Large Eddy Simulation (LES) is used as reference for the Unsteady Reynolds-Averaged Navier–Stokes (URANS) computations. A methodology for the uncertainty quantification in engineering applications with a preceding mesh convergence study and sensitivity analysis is presented. By taking the LES as a reference, the results indicate that URANS is able to predict the underlying mixing process at Ra=2×109 and the variability of the result variables due to parameter uncertainties.

Transient conjugate natural convection heat transfer in a differentially-heated square cavity with a partition of finite thickness and thermal conductivity

The transient conjugate natural convection heat transfer in a differentially-heated cavity with a partition of finite thickness and thermal conductivity are investigated numerically over the range of the Rayleigh number from 103 to 108, the thermal conductivity ratio of partition to that of fluid from 0.1 to 1000, and the dimensionless partition thickness from 0.05 to 0.2. An analysis of the obtained temperature contours and profiles, the time for the onset of stratification and the Nusselt number shows that the thermal conductivity ratio effect is significant only over the range of 0.1–10, when the role played by the partition changes, whereas the effect becomes negligible as the thermal conductivity ratio is very large (100 or beyond). It is also found that the scaling relations developed for the non-partitioned cavity are found to be applicable for the partitioned cavity. The results further show that the effect of the partition thickness on heat transfer is significant mainly when the thermal conductivity ratio is small.

Variable property DNS of differentially heated cavities filled with air

Direct numerical simulations (DNS) of the thermally-driven flow of air inside differentially heated cavities (DHC) are presented. The variation of air properties is taken into account using the low-Mach approximation, to obtain solutions outside the limits of the Oberbeck–Boussinesq (OB) approximation. The effects of the cavity’s aspect-ratio A and large temperature differences ΔT were investigated over the range 1 ≤ A ≤ 8 and ΔT ≤ 720 K. The Rayleigh and Prandtl numbers were set at Ra=109 and Pr=0.7, considering a reference temperature of T0=600 K. Time-averaged and r.m.s. statistics of the temperature field along with other derived quantities are presented and discussed. It is found that the time-averaged temperature fields vary significantly between non-Oberbeck–Boussinesq (NOB) and OB cases for larger aspect-ratios. This is also true for the instantaneous temperature and temperature r.m.s. fields which demonstrate significant qualitative differences. In addition, as the temperature difference increases and the property variations become more intense, the boundary layers at the vertical walls become turbulent at lower positions. The relocation of the laminar-turbulent transition point is found to be strongly dependent on the cavity’s aspect-ratio. An explanation of this phenomenon is given, based on the disruption of the vertical boundary layers by horizontal streams originating from the downstream part of the vertical walls.

Large Eddy simulations of particulate flows inside a square differentially heated cavity at Rayleigh numbers up to 1011

The Differentially Heated Cavity (DHC) has often served as a suitable geometric model for naturally driven particulate flows inside closed volumes. While providing deep insights of the flow dynamics, 3D DNS or 3D LES simulations of DHC flows are very time-consuming and their potential extension to higher Rayleigh (Ra) numbers typical of room dimensions is problematic. In this study, therefore, a 2D-LES Euler-Lagrange approach is used to predict turbulent particle transport in a DHC.We first validate our predictions against a 2D DNS database at Ra 109 and 1010 with particles having diameters greater than 15 μm. We show that our LES results are in very agreement with the DNS data. In a second step, we extend our simulations to a fully turbulent Ra number 1011 and particle diameters between 0.5 and 10 m. Details are provided on the particle deposition locations and airborne concentration decay rate with time. We show in particular that as the flow becomes more turbulent, the particle settling rates approach those predicted by the simple stirred settling model.

Heat transfer modification induced by a localized thermal disturbance in a differentially-heated cavity

Numerical investigation of a natural convection flow with a localized thermal disturbance is presented here. The configuration of a differentially heated cavity is considered with air as working fluid. In this study, the initial flow regime is steady and close to the transition to unsteadiness. Different cases of local wall temperature disturbances are tested in a thin area at the onset of the hot vertical boundary layer. These cases are distinguished by the time-averaged temperature of this area (higher or lower than the hot wall temperature) and by their temporal evolution (steady or periodic). In cases with a periodic disturbance, the imposed frequency corresponds to the first frequency emerging in the unsteady regime. The results show the spread of temperature fluctuations across the whole cavity with the periodic disturbance, in particular near the upper corner of the cavity. The hot steady disturbance trigs the onset of time-dependent flow. Moreover, the local modification of the hot wall temperature has an impact on global heat transfer: about 16% downstream the disturbance area and about 2% on the opposite cold wall.

Whole field measurements to understand the effect of nanoparticle concentration on heat transfer rates in a differentially-heated fluid layer

Experimental study on natural convection in a nanofluid-filled differentially heated cavity has been presented. Experiments have been conducted in an octagonal cavity with water and Al2O3/water-based dilute nanofluids of varying concentrations. A Mach Zehnder interferometer has been employed to record the projection data of convective field from four view angles (0, 45, 90 and 135°). The two-dimensional temperature fields determined through the quantitative analysis of the interferometric images have been employed to reconstruct the local field information using the principles of tomography. Results of the three-dimensional reconstructions clearly brought out the mechanisms of possible fluid movement in the differentially-heated cavity and its dependence on nanoparticle concentration. Near wall surface distributions of temperature fields as well as local Nusselt numbers indicated towards possible breakdown of large scale fluid structures into small length scale multiple roll-like circulatory loops at higher volumetric concentrations of dilute nanofluids. Local disturbances thus induced in the fluid layer due to the addition of nanoparticles resulted into better fluid mixing, which in turn led to an enhancement in the heat transfer rates with increasing concentration of nanofluids. Surface plots of Nusselt numbers obtained in the vicinity of the two thermally active walls of the cavity established an overall energy balance in the fluid layer.

Buoyancy-induced Lagrangian chaos: the differentially-heated cavity revisited

Natural convection plays a key role in fluid dynamics owing to its ubiquitous presence in nature and industry. Buoyancy-driven flows are prototypical systems in the study of thermal instabilities and pattern formation. The differentially-heated cavity problem has been widely studied for the investigation of buoyancy-induced oscillatory flow. However, far less attention has been devoted to the three-dimensional Lagrangian transport properties in such flows. This study seeks to address this by investigating Lagrangian transport in the steady flow inside differentially-heated cavities. The theoretical and numerical analysis expands on previously reported similarities between the current flow and lid-driven flows. First results reveal that the convective terms in the momentum and energy balances cause non-trivial (and potentially chaotic) Lagrangian transport.

Enhanced thermal energy transport using adiabatic block inside lid-driven cavity

Most of the energy related applications are involved with heat transfer and fluid flow, and the efficient utilization of energy system is always a matter of great importance. With a simple flow geometry, the present work is devoted to report a better thermal energy transfer utilizing an adiabatic block in a sidewalls moving, differentially-heated cavity. The study demonstrates the effective role of the adiabatic block on energy transport from source to sink. The adiabatic block, depending on the situations, both favors and hinders overall heat transfer of the system. The size of the block decides the modality of thermal energy transfer. In this work, different speeds and configurations of wall motion are investigated exhaustively to assess the extent of heat transfer augmentation and the optimal block sizes. The results indicate that, up to a certain block size, the thermal energy transport of this cavity enhances. Heat transfer augmentation is remarkably high for opposing flow situation. The dynamics of energy flow from the source to the sink is presented using heatfunction that reveals the evolution of energy recirculation cells in the cavity. The presence of an adiabatic block potentially suppresses this energy recirculation. The evolved vortical flow structure in the cavity is explained using elliptical and hyperbolic points. The study is further extended to include the impact of cavity inclination on the thermal performance.

Interferometric study of natural convection in a differentially-heated cavity with Al2O3–water based dilute nanofluids

Heat transfer characteristics of dilute nanofluids under natural convection regime have been experimentally studied. The buoyancy-driven convection has been set-up in a differentially heated cavity containing basefluid (de-ionized water) and Al2O3/water-based dilute nanofluids. Temperature difference has been employed across the two horizontal walls of cavity, the side walls being thermally insulated. Experiments have been performed for four volumetric concentrations (0.01%, 0.02%, 0.03% and 0.04%) of nanofluids. Projection data of the temperature field has been recorded using a Mach–Zehnder interferometer. Results have been presented in the form of interferograms of the convective field, two-dimensional distributions and variations of heat transfer coefficients as a function of nanofluid concentrations and temperature differences. Results of the study reveal a strong dependence of convective field on the concentration of nanofluids. At low Rayleigh numbers, while the heat transfer through central core region of the cavity was predominately through conduction for de-ionized water, significant convective effects were seen in the case of nanofluids. At higher values of driving potential, strong convective movements in the entire fluid layer were observed irrespective of the type of fluid employed. In nanofluid based experiments, well-defined roll-like convective structures were to be seen with an increase in cavity temperature difference. Time-dependent movement of these dominant structures was observed. Spectral analysis of the intensity-time signal revealed an increasing trend in the frequency of oscillation with an increase in the concentration of nanofluid for any given value of ΔT. The experiments revealed that at higher driving potential, with increasing concentration of nanoparticles, the bigger structures continuously form and break into smaller roll-like structures, thus indicating better mixing in fluid layer, leading to higher heat transfer rates.

Coupling of turbulent natural convection with radiation in an air-filled differentially-heated cavity at Ra = 1.5 × 109

This paper deals with the influence of radiation on natural convection airflows in confined areas. The investigated configuration is a square differentially-heated cavity at Ra=1.5×109. Two dimensional LES computations have been carried out using a specific subgrid model for the thermal diffusivity and taking into account gas and wall radiation. Radiation within the fluid (due to the presence of water vapor in humid air) is considered using the SLW model developed by Denison and Webb and the Discrete Ordinate Method (S8 quadrature). Comparisons are carried out for four cases (without radiation, wall radiation only, gas radiation only and combined gas and wall radiation) and compared in terms of velocity and temperature fields as well as turbulent quantities (kinetic energy, turbulence intensity). Global heat transfer is also investigated and a comparison is made between the different cases.

Numerical solutions for the fluid flow and the heat transfer of viscoplastic-type non-Newtonian fluids

The aim of this work is to provide numerical solutions for the fluid flow and the heat transfer generated in closed systems containing viscoplastic-type non-Newtonian fluids. A lid driven cavity (LDC) and a differentially heated cavity (DHC) are used as test cases. These numerical solutions can be an appropriate tool for verifying CFD codes which have been developed or adapted to deal with this kind of non-Newtonian fluids. In order to achieve this objective, an in-house CFD code has been implemented and correctly verified by the method of manufactured solutions and by some numerical solutions too. Furthermore, a high-performance CFD code (Termo Fluids S.L.) has been adapted and properly verified, by the corresponding numerical solutions, to deal with this kind of non-Newtonian fluids.The viscoplastic behaviour of certain non-Newtonian fluids will be generated from a viscous stress which has been defined by a potential-type rheological law. The pseudoplastic and dilatant behaviours will be studied. On this matter, the influence of different physical aspects on the numerical simulations will be analysed, e.g. different exponent values in the potential-type rheological law and different values of the non-dimensional numbers. Moreover, the influence of different numerical aspects on the numerical simulations will also be analysed, e.g. unstructured meshes, conservative numerical schemes and more efficient and parallel algorithms and solvers.

Experimental investigations in an air-filled differentially-heated cavity at large Rayleigh Numbers

A large-scale experimental differentially heated cavity was built and instrumented. Rayleigh numbers up to 1.2×1011 can be obtained with a temperature difference, ΔT = 20°C, between the hot and cold walls leaning in the range of validity of the Boussinesq approximation. Previous data obtained locally for mean velocity by 2D LDV in the range give rise to questions regarding the general air flow circulation in the cavity. Particularly, a downstream flow along the vertical boundary layer was observed. This reverse flow caused by the temperature stratification outside this layer is not present in the upstream parts and was not previously observed in smaller cavities. The question of the global circulation in this cavity is thus posed. Evolution laws providing Nusselt numbers are also given and when possible compared to the literature for a large range of Rayleigh numbers.

Experimental investigation of buoyant flows in inclined differentially heated cavities

This experimental investigation focuses on the effects of angle of inclination on buoyancy-driven flows inside tall, rectangular, differentially-heated cavities. It considers a rectangular cavity with an aspect ratio of 28.6, with its two long sides maintained at different temperatures and the two short, end-walls, thermally insulated. The spanwise aspect ratio is 6.82 and the side walls are also thermally insulated. The Rayleigh number, based on the temperature difference and spacing between the long sides, is 0.86×106 for most cases and the working fluid is air (Prandtl number 0.71). Experimental data, for the flow and the thermal fields, using laser Doppler anemomentry and thermocouple traverses respectively, are presented for the cavity inclined at 60° and 15° to the horizontal, for both stable (the hot surface being the upper surface) and unstable orientations. The 15° stable case is investigated at a higher Rayleigh number of 1.54×106 and some additional data for the 15° unstable case are also presented at this higher value of Rayleigh number. For moderate angles of inclination, the flow is two-dimensional and the effects of inclination are primarily confined to the fluctuating fields. For large angles of inclination, the flow becomes three-dimensional. In the unstable 15° angle of inclination case a set of four longitudinal vortices are formed over the entire length of the cavity, with four counter-rotating re-circulation cells within the cross-section parallel to the thermally active walls. The stable 15° angle of inclination leads to the formation of two longitudinal vortices and two re-circulation cells. At the 15° angle (stable and unstable), the enhanced mixing leads to uniform temperature in the cavity core and thus to only minor deviations from two-dimensionality in the thermal field. A modest rise in Rayleigh number, in the 15° unstable case, does not affect the mean motion, but causes an increase in the normalised turbulence intensities.

Experimental determination of first bifurcations to unsteady natural convection in a differentially-heated cavity tilted from 0° to 180°

This paper focuses on an experimental study of the natural convection unsteadiness occurring in an air-filled cavity having two opposite walls respectively heated and cooled at constant and uniform temperature. The other walls are made of insulating materials. The cavity can be tilted in order to obtain an angle of inclination, θ, from 0° (heating from below) to 180° (heating from above). For these extreme angles, the two active walls are horizontal. For each investigated angle of inclination, instantaneous temperature measurements have been carried out in selected areas where temperature signal should became unsteady first, when the temperature difference between the two plates was increased. The location where fluctuations are close to the maximum was then identified. A critical value of temperature difference, ΔT, was calculated after extrapolation of PSD obtained for several values of ΔT. It was highlighted, that for ΔT lower than this critical value, the power spectral density was close to 0 and grew like (ΔT)0.5 for ΔT greater than this critical value. The same critical value was obtained when increasing or decreasing ΔT, showing that it corresponds to a supercritical bifurcation. Spectral analyses reveal that for all the angles of tilt, the first bifurcation appears at the specific and unique value 8.5×107 of a modified Rayleigh number, defined from H∗ equal to H/[tan(θ/2)]0.5, with H referring to the height of the cavity. In addition, for all the tilt angles, the measured frequencies describe the successive bifurcations occurring until turbulence is encountered with the temperature increase. The exception to this is the angle of 180° where the flow remains always in a steady state. Visualizations have been performed in order to characterise flow patterns obtained between two successive bifurcations. Different class of natural convection flows were then identified, showing Rayleigh–Bénard flow types, boundary layer flows, or typical structures obtained with stably stratified fluids. Time oscillations are also due to completely different modes of unsteadiness: thermal instabilities (gravity or Kelvin – Helmholtz waves) or dynamical instabilities (Tollmien–Schlichting progressive waves).

DNS of buoyancy-driven flows and Lagrangian particle tracking in a square cavity at high Rayleigh numbers

In this work we investigate numerically particle deposition in the buoyancy driven flow of the differentially heated cavity (DHC). We consider two values of the Rayleigh number ( Ra = 10 9, 10 10) and three values of the particle diameter ( d p = 15, 25, 35 [μm]). We consider the cavity filled with air and particles with the same density of water ρ w = 1000 [kg/m 3] (aerosol). We use direct numerical simulations (DNS) for the continuous phase, and we solve transient Navier–Stokes and energy transport equations written in an Eulerian framework, under the Boussinesq approximation, for the viscous incompressible Newtonian fluid with constant Prandtl number ( Pr = 0.71). First- and second-order statistics are presented for the continuous phase as well as important quantities like turbulent kinetic energy (TKE) and temperature variance with the associated production and dissipation fields. The TKE production shows different behaviour at the two Rayleigh numbers. The Lagrangian approach has been chosen for the dispersed phase description. The forces taken into account are drag, gravity, buoyancy, lift and thermophoresis. A first incursion in the sedimentation mechanisms is presented. Current results indicate that the largest contribution to particle deposition is caused by gravitational settling, but a strong recirculating zone, which liftoffs and segregates particles, contributes to decrease settling. Deposition takes place mostly at the bottom wall. The influence of lift and thermophoretic forces on particle removal is discussed in detail. Indeed, it is shown that the lift is responsible of particle deposition on the vertical cold surface.

Proper orthogonal decomposition of a fully confined cubical differentially heated cavity flow at Rayleigh number Ra = 109

Proper orthogonal decomposition is used to educe fundamental velocity and temperature coherent structures in the fully confined cubical three-dimensional differentially heated cavity (DHC) flow. Among other linear decompositions, the POD is optimal in the sense that it provides a set of modes that captures the largest amount of energy contained in the snapshot ensemble. We present here preliminary results of the first empirical eigenfunctions that account up to 95% of the total energy of the ensemble. The database is made of 200 snapshots obtained by means of Direct Numerical Simulation (DNS) at Rayleigh Ra=109. The results are in good agreement with previous observations of coherent structures identified with λ2 criterion, confirming the importance of the elongated spanwise structures (located downstream the break up of the laminar vertical boundary layers) for the description/modeling of the turbulent heat flux. The basis functions that account for the largest part of the turbulent heat flux are not made of the most energetic POD empirical eigenfunctions. In appears that the spatial structures which contain the largest fraction of the turbulent heat transfer correspond to the POD modes characterized by the presence of spanwise elongated vortices at the vertical active walls where temperature and velocity eigenfunctions are spatially strongly correlated.