Linear and Nonlinear Stability Analyses of Double-Diffusive Convection in a Vertical Brinkman Porous Enclosure under Soret and Dufour Effects

Analytical and numerical investigations were performed to study the influence of the Soret and Dufour effects on double-diffusive convection in a vertical porous layer filled with a binary mixture and subject to horizontal thermal and solute gradients. In particular, the study was focused on the effect of Soret and Dufour diffusion on bifurcation types from the rest state toward steady convective state, and then toward oscillatory convective state. The Brinkman-extended Darcy model and the Boussinesq approximation were employed to model the convective flow within the porous layer. Following past laboratory experiments, the investigations dealt with the particular situation where the solutal and thermal buoyancy forces were equal but acting in opposite direction to favor the possible occurrence of the rest state condition. For this situation, the onset of convection could be either supercritical or subcritical and occurred at given thresholds and following various bifurcation routes. The analytical investigation was based on the parallel flow approximation, which was valid only for a tall porous layer. A numerical linear stability analysis of the diffusive and convective states was performed on the basis of the finite element method. The thresholds of supercritical, RTCsup, and overstable, RTCover, convection were computed. In addition, the stability of the established convective flow, predicted by the parallel flow approximation, was studied numerically to predict the onset of Hopf’s bifurcation, RTCHopf, which marked the transition point from steady toward unsteady convective flows; a route towards the chaos. To support the analytical analyses of the convective flows and the numerical stability methodology and results, nonlinear numerical solutions of the full governing equations were obtained using a second-order finite difference method. Overall, the Soret and Dufour effects were seen to affect significantly the thresholds of stationary, overstable and oscillatory convection. The Hopf bifurcation was marked by secondary convective flows consisting of superposed vertical layers of opposite traveling waves. A good agreement was found between the predictions of the parallel flow approximation, the numerical solution and the linear stability results.

Dynamics of a High-Order Generalized Lorenz Model for Magnetoconvection

In this paper, we present a 6D generalized Lorenz model for magnetoconvection of an electrically conducting viscous fluid layer subjected to horizontally imposed uniform magnetic field. It generalizes the 4D generalized Lorenz model of Macek and Strumik [Phys. Rev. E 82, 027301 (2010)] taking into account high-wavenumber vertical Fourier modes of the temperature profile. These additional modes not only increase the feedback loop of the system but also subsequently affect the transitional processes. The boundedness, stability of solutions, bifurcation patterns enroute to chaos for the new 6D model are explored. Studies reveal that the stability of the quiescent state does not alter. But the stability of the steady convective state differs in comparison to the 4D model. The regions of aperiodic oscillation are suppressed which results in stabilization of the convective motion. Some new organized periodic structures embedded in chaotic domain appear in parameter space of the 6D model, and the transitional route to hyperchaos is altered owing to the inclusion of the high-order modes.

Evaluation of the Global S-Entropy Production in Membrane Transport of Aqueous Solutions of Hydrochloric Acid and Ammonia

The results of experimental studies of volume osmotic fluxes (Jvkr) and fluxes of dissolved substances (Jkr) in a system containing a synthetic Nephrophan® membrane (Orwo VEB Filmfabrik, Wolfen, Germany) set in a horizontal plane are presented. The membrane separated water and aqueous HCl or ammonia solutions or aqueous ammonia and HCl solutions. It was found that for the homogeneity conditions of the solutions Jvk and Jk depend only on the concentration and composition of the solutions. For concentration polarization conditions (where concentration boundary layers are created on both sides), Jvkr and Jkr depend on both the concentration and composition of the solutions and the configuration of the membrane system. The obtained results of the Jvk and Jk flux studies were used to assess the global production of entropy for the conditions of homogeneity of solutions (ΦSk), while Jvkr and Jkr—to assess the global production of entropy for concentration polarization conditions (ΦSkr). In addition, the diffusion-convective effects and the convection effect in the global source of entropy were calculated. The concentration polarization coefficient ζir was related to modified concentration Rayleigh number, e.g., the parameter controlling the transition from non-convective (diffusive) to convective state. This number acts as a switch between two states of the concentration field: convective (with a higher entropy source value) and non-convective (with a lower entropy source value). The operation of this switch indicates the regulatory role of earthly gravity in relation to membrane transport.

Development of an Unmanned Aerial Vehicle for the Measurement of Turbulence in the Atmospheric Boundary Layer

This paper describes the components and usage of an unmanned aerial vehicle developed for measuring turbulence in the atmospheric boundary layer. A method of computing the time-dependent wind speed from a moving velocity sensor data is provided. The physical system built to implement this method using a five-hole probe velocity sensor is described along with the approach used to combine data from the different on-board sensors to allow for extraction of the wind speed as a function of time and position. The approach is demonstrated using data from three flights of two unmanned aerial vehicles (UAVs) measuring the lower atmospheric boundary layer during transition from a stable to convective state. Several quantities are presented and show the potential for extracting a range of atmospheric boundary layer statistics.

The Heated Condensation Framework. Part I: Description and Southern Great Plains Case Study

This study extends the heated condensation framework (HCF) presented in Tawfik and Dirmeyer to include variables for describing the convective background state of the atmosphere used to quantify the contribution of the atmosphere to convective initiation within the context of land–atmosphere coupling. In particular, the ability for the full suite of HCF variables to 1) quantify the amount of latent and sensible heat energy necessary for convective initiation, 2) identify the transition from moistening advantage to boundary layer growth advantage, 3) identify locally originating convection, and 4) compare models and observations, directly highlighting biases in the convective state, is demonstrated. These capabilities are illustrated for a clear-sky and convectively active day over the Atmospheric Radiation Measurement Program Southern Great Plains central station using observations, the Rapid Update Cycle (RUC) operational model, and the North American Regional Reanalysis (NARR). The clear-sky day had a higher and unattainable convective threshold, making convective initiation unlikely. The convectively active day had a lower threshold that was attained by midafternoon, reflecting local convective triggering. Compared to observations, RUC tended to have the most difficulty representing the convective state and captured the threshold for the clear-sky case only because of compensating biases in the moisture and temperature profiles. Despite capturing the observed moisture profile very well, a stronger surface inversion in NARR returned overestimates in the convective threshold. The companion paper applies the HCF variables introduced here across the continental United States to examine the climatological behavior of convective initiation and local land–atmosphere coupling.

Combined Spectral-Perturbation Approach for Systematic Mode Selection in Thermal Convection

A nonlinear spectral approach is proposed to simulate the post critical convective state for thermogravitational instability in a Newtonian fluid layer heated from below. The spectral methodology consists of expanding the flow and temperature fields periodically along the layer, and using orthonormal shape functions in the transverse direction. The Galerkin projection is then implemented to generate the equations for the expansion coefficients. Since most of the interesting bifurcation picture is close to criticality, a perturbation approach is developed to solve the nonlinear spectral system in the weakly post critical range. To leading order, the Lorenz model is recovered. The problem is also solved using amplitude equations for comparison. The similarity and difference among the three models are emphasized.

Detailed Measurements of End-Wall Heat Transfer Coefficients of Square Pin-Fin Heat Sink for LED Lamp at Forced Convective State

The device made of fan and pin-fin heat sink should be a powerful heat sink for LED lamp. This study used transient liquid crystal experimentation to measure the end-wall heat transfer coefficient of linearly arrayed square pin array in the rectangular channel, and discussed the influence of axial spacing on heat transfer. The air was used as operating fluid, and the square pin size was 8 mm (d) × 8 mm (d) × 64 mm (Hf), arrayed in a 240 mm (L) × 120 mm (W) × 64 mm (H) rectangular channel. The relative lateral spacing (XT=ST/d) was set as 3, and the relative axial spacing (XL=SL/d=1.88~5) and the Reynolds number (Re=11047~17937) were changed. Considering the end-wall area, the average Nusselt number with square pin was 1.46~2.58 times of that without square pin, and the square pin array of XL= 3.75 had the maximum end-wall heat transfer gain.

INFLUENCE OF SEDIMENTATION ON CONVECTIVE INSTABILITIES IN COLLOIDAL SUSPENSIONS

We investigate theoretically the bifurcation scenario for colloidal suspensions subject to a vertical temperature gradient taking into account the effect of sedimentation. In contrast to molecular binary mixtures, here the thermal relaxation time is much shorter than that for concentration fluctuations. This allows for differently prepared ground states, where a concentration profile due to sedimentation and/or the Soret effect has been established or not. This gives rise to different linear instability behaviors, which are manifest in the temporal evolution into the final, generally stationary convective state. In a certain range, above a rather high barometric number there is a coexistence between the quiescent state and the stationary convective one, allowing for a hysteretic scenario.