Theoretical and numerical analyses of convective instability in porous media with upward throughflow

Exact analytical solutions have been obtained for a hydrothermal system consisting of a horizontal porous layer with upward throughflow. The boundary conditions considered are constant temperature, constant pressure at the top, and constant vertical temperature gradient, constant Darcy velocity at the bottom of the layer. After deriving the exact analytical solutions, we examine the stability of the solutions using linear stability theory and the Galerkin method. It has been found that the exact solutions for such a hydrothermal system become unstable when the Rayleigh number of the system is equal to or greater than the corresponding critical Rayleigh number. For small and moderate Peclet numbers (Pe less than or equal to 6), an increase in upward throughflow destabilizes the convective flow in the horizontal layer. To confirm these findings, the finite element method with the progressive asymptotic approach procedure is used to compute the convective cells in such a hydrothermal system. Copyright (C) 1999 John Wiley & Sons, Ltd.

Theoretical and numerical analyses of convective instability in porous media with temperature-dependent viscosity

Exact analytical solutions of the critical Rayleigh numbers have been obtained for a hydrothermal system consisting of a horizontal porous layer with temperature-dependent viscosity. The boundary conditions considered are constant temperature and zero vertical Darcy velocity at both the top and bottom of the layer. Not only can the derived analytical solutions be readily used to examine the effect of the temperature-dependent viscosity on the temperature-gradient driven convective flow, but also they can be used to validate the numerical methods such as the finite-element method and finite-difference method for dealing with the same kind of problem. The related analytical and numerical results demonstrated that the temperature-dependent viscosity destabilizes the temperature-gradient driven convective flow and therefore, may affect the ore body formation and mineralization in the upper crust of the Earth. Copyright (C) 2003 John Wiley Sons, Ltd.

Symmetric stability of compressible zonal flows on a generalized equatorial β plane

Sufficient conditions are derived for the linear stability with respect to zonally symmetric perturbations of a steady zonal solution to the nonhydrostatic compressible Euler equations on an equatorial � plane, including a leading order representation of the Coriolis force terms due to the poleward component of the planetary rotation vector. A version of the energy–Casimir method of stability proof is applied: an invariant functional of the Euler equations linearized about the equilibrium zonal flow is found, and positive definiteness of the functional is shown to imply linear stability of the equilibrium. It is shown that an equilibrium is stable if the potential vorticity has the same sign as latitude and the Rayleigh centrifugal stability condition that absolute angular momentum increase toward the equator on surfaces of constant pressure is satisfied. The result generalizes earlier results for hydrostatic and incompressible systems and for systems that do not account for the nontraditional Coriolis force terms. The stability of particular equilibrium zonal velocity, entropy, and density fields is assessed. A notable case in which the effect of the nontraditional Coriolis force is decisive is the instability of an angular momentum profile that decreases away from the equator but is flatter than quadratic in latitude, despite its satisfying both the centrifugal and convective stability conditions.

Assessment of Convective Activity Using Stability Indices as Inferred from Radiosonde and MODIS Data

The combined use of both radiosonde data and three-dimensional satellite derived data over ocean and land is useful for a better understanding of atmospheric thermodynamics. Here, an attempt is made to study the ther-modynamic structure of convective atmosphere during pre-monsoon season over southwest peninsular India utilizing satellite derived data and radiosonde data. The stability indices were computed for the selected stations over southwest peninsular India viz: Thiruvananthapuram and Cochin, using the radiosonde data for five pre- monsoon seasons. The stability indices studied for the region are Showalter Index (SI), K Index (KI), Lifted In-dex (LI), Total Totals Index (TTI), Humidity Index (HI), Deep Convective Index (DCI) and thermodynamic pa-rameters such as Convective Available Potential Energy (CAPE) and Convective Inhibition Energy (CINE). The traditional Showalter Index has been modified to incorporate the thermodynamics over tropical region. MODIS data over South Peninsular India is also used for the study. When there is a convective system over south penin-sular India, the value of LI over the region is less than −4. On the other hand, the region where LI is more than 2 is comparatively stable without any convection. Similarly, when KI values are in the range 35 to 40, there is a possibility for convection. The threshold value for TTI is found to be between 50 and 55. Further, we found that prior to convection, dry bulb temperature at 1000, 850, 700 and 500 hPa is minimum and the dew point tem-perature is a maximum, which leads to increase in relative humidity. The total column water vapor is maximum in the convective region and minimum in the stable region. The threshold values for the different stability indices are found to be agreeing with that reported in literature.

Convective transport and stability in films of binary mixtures

Thin polymer films are increasingly used in advanced technological applications. The use of these films as coatings is often limited by their lack of stability due to their wettability properties on the substrates

Stability, viscous dissipation and local thermal non-equilibrium in fluid saturated porous media

In this thesis, the field of study related to the stability analysis of fluid saturated porous media is investigated. In particular the contribution of the viscous heating to the onset of convective instability in the flow through ducts is analysed. In order to evaluate the contribution of the viscous dissipation, different geometries, different models describing the balance equations and different boundary conditions are used. Moreover, the local thermal non-equilibrium model is used to study the evolution of the temperature differences between the fluid and the solid matrix in a thermal boundary layer problem. On studying the onset of instability, different techniques for eigenvalue problems has been used. Analytical solutions, asymptotic analyses and numerical solutions by means of original and commercial codes are carried out.

Convective instabilities in two superposed horizontal liquid layers heated laterally.

This work is devoted to the theoretical study of the stability of two superposed horizontal liquid layers bounded by two solid planes and subjected to a horizontal temperature gradient. The liquids are supposed to be immiscible with a nondeformable interface. The forces acting on the system are buoyancy and interfacial tension. Four different flow patterns and temperature profiles are found for the basic state. A linear perturbative analysis with respect to two- and three-dimensional perturbations reveals the existence of three kinds of patterns. Depending on the relative height of both liquids several situations are predicted: either wave propa- gation from cold to the hot regions, or waves propagating in the opposite direction or still stationary longitu- dinal rolls. The behavior of three different pairs of liquids which have been used in experiments on bilayers under vertical gradient by other authors have been examined. The instability mechanisms are discussed and a qualitative interpretation of the different behaviors exhibited by the system is provided. In some configurations it is possible to find a codimension-two point created by the interaction of two Hopf modes with different frequencies and wave numbers. These results suggest to consider two liquid layers as an interesting prototype ? nard-Marangoni problem.

Theoretical investigation of convective instability in inclined and fluid-saturated three-dimensional fault zones.

The convective instability of pore-fluid flow in inclined and fluid-saturated three-dimensional fault zones has been theoretically investigated in this paper. Due to the consideration of the inclined three-dimensional fault zone with any values of the inclined angle, it is impossible to use the conventional linear stability analysis method for deriving the critical condition (i.e., the critical Rayleigh number) which can be used to investigate the convective instability of the pore-fluid flow in an inclined three-dimensional fault zone system. To overcome this mathematical difficulty, a combination of the variable separation method and the integration elimination method has been used to derive the characteristic equation, which depends on the Rayleigh number and the inclined angle of the inclined three-dimensional fault zone. Using this characteristic equation, the critical Rayleigh number of the system can be numerically found as a function of the inclined angle of the three-dimensional fault zone. For a vertically oriented three-dimensional fault zone system, the critical Rayleigh number of the system can be explicitly derived from the characteristic equation. Comparison of the resulting critical Rayleigh number of the system with that previously derived in a vertically oriented three-dimensional fault zone has demonstrated that the characteristic equation of the Rayleigh number is correct and useful for investigating the convective instability of pore-fluid flow in the inclined three-dimensional fault zone system. The related numerical results from this investigation have indicated that: (1) the convective pore-fluid flow may take place in the inclined three-dimensional fault zone; (2) if the height of the fault zone is used as the characteristic length of the system, a decrease in the inclined angle of the inclined fault zone stabilizes the three-dimensional fundamental convective flow in the inclined three-dimensional fault zone system; (3) if the thickness of the stratum is used as the characteristic length of the system, a decrease in the inclined angle of the inclined fault zone destabilizes the three-dimensional fundamental convective flow in the inclined three-dimensional fault zone system; and that (4) the shape of the inclined three-dimensional fault zone may affect the convective instability of pore-fluid flow in the system. (C) 2004 Published by Elsevier B.V.

Transition in convective flows heated internally

The stability of internally heated convective flows in a vertical channel under the influence of a pressure gradient and in the limit of small Prandtl number is examined numerically. In each of the cases studied the basic flow, which can have two inflection points, loses stability at the critical point identified by the corresponding linear analysis to two-dimensional states in a Hopf bifurcation. These marginal points determine the linear stability curve that identifies the minimum Grashof number (based on the strength of the homogeneous heat source), at which the two-dimensional periodic flow can bifurcate. The range of stability of the finite amplitude secondary flow is determined by its (linear) stability against three-dimensional infinitesimal disturbances. By first examining the behavior of the eigenvalues as functions of the Floquet parameters in the streamwise and spanwise directions we show that the secondary flow loses stability also in a Hopf bifurcation as the Grashof number increases, indicating that the tertiary flow is quasi-periodic. Secondly the Eckhaus marginal stability curve, that bounds the domain of stable transverse vortices towards smaller and larger wavenumbers, but does not cause a transition as the Grashof number increases, is also given for the cases studied in this work.

Idealized modeling of the role of stability and shear on mesoscale gravity wave evolution

Mesoscale Gravity Waves (MGWs) are large pressure perturbations that form in the presence of a stable layer at the surface either behind Mesoscale Convective Systems (MCSs) in summer or over warm frontal surfaces behind elevated convection in winter. MGWs are associated with damaging winds, moderate to heavy precipitation, and occasional heat bursts at the surface. The forcing mechanism for MGWs in this study is hypothesized to be evaporative cooling occurring behind a convective line. This evaporatively-cooled air generates a downdraft that then depresses the surface-based stable layer and causes pressure decreases, strong wind speeds and MGW genesis. Using the Weather Research and Forecast Model (WRF) version 3.0, evaporative cooling is simulated using an imposed cold thermal. Sensitivity studies examine the response of MGW structure to different thermal and shear profiles where the strength and depth of the inversion are varied, as well as the amount of wind shear. MGWs are characterized in terms of response variables, such as wind speed perturbations (U'), temperature perturbations (T'), pressure perturbations (P'), potential temperature perturbations (Θ'), and the correlation coefficient (R) between U' and P'. Regime Diagrams portray the response of MGW to the above variables in order to better understand the formation, causes, and intensity of MGWs. The results of this study indicate that shallow, weak surface layers coupled with deep, neutral layers above favor the formation of waves of elevation. Conversely, deep strong surface layers coupled with deep, neutral layers above favor the formation of waves of depression. This is also the type of atmospheric setup that tends to produce substantial surface heating at the surface.

On the Stability of Supersonic Boundary Layers with Injection

The problem of supersonic flow over a 5 degree half-angle cone with injection of gas through a porous section on the body into the boundary layer is studied experimentally. Three injected gases are used: helium, nitrogen, and RC318 (octafluorocyclobutane). Experiments are performed in a Mach 4 Ludwieg tube with nitrogen as the free stream gas. Shaping of the injector section relative to the rest of the body is found to admit a "tuned" injection rate which minimizes the strength of shock waves formed by injection. A high-speed schlieren imaging system with a framing rate of 290 kHz is used to study the instability in the region of flow downstream of injection, referred to as the injection layer. This work provides the first experimental data on the wavelength, convective speed, and frequency of the instability in such a flow. The stability characteristics of the injection layer are found to be very similar to those of a free shear layer. The findings of this work present a new paradigm for future stability analyses of supersonic flow with injection.

Estimation of Convective Extreme Events over Germany based on Large Scale Parameters

Strong convective events can produce extreme precipitation, hail, lightning or gusts, potentially inducing severe socio-economic impacts. These events have a relatively small spatial extension and, in most cases, a short lifetime. In this study, a model is developed for estimating convective extreme events based on large scale conditions. It is shown that strong convective events can be characterized by a Weibull distribution of radar-based rainfall with a low shape and high scale parameter value. A radius of 90km around a station reporting a convective situation turned out to be suitable. A methodology is developed to estimate the Weibull parameters and thus the occurrence probability of convective events from large scale atmospheric instability and enhanced near-surface humidity, which are usually found on a larger scale than the convective event itself. Here, the probability for the occurrence of extreme convective events is estimated from the KO-index indicating the stability, and relative humidity at 1000hPa. Both variables are computed from ERA-Interim reanalysis. In a first version of the methodology, these two variables are applied to estimate the spatial rainfall distribution and to estimate the occurrence of a convective event. The developed method shows significant skill in estimating the occurrence of convective events as observed at synoptic stations, lightning measurements, and severe weather reports. In order to take frontal influences into account, a scheme for the detection of atmospheric fronts is implemented. While generally higher instability is found in the vicinity of fronts, the skill of this approach is largely unchanged. Additional improvements were achieved by a bias-correction and the use of ERA-Interim precipitation. The resulting estimation method is applied to the ERA-Interim period (1979-2014) to establish a ranking of estimated convective extreme events. Two strong estimated events that reveal a frontal influence are analysed in detail. As a second application, the method is applied to GCM-based decadal predictions in the period 1979-2014, which were initialized every year. It is shown that decadal predictive skill for convective event frequencies over Germany is found for the first 3-4 years after the initialization.

Comparison Of Postoperative Stability Of Three Rigid Internal Fixation Techniques After Sagittal Split Ramus Osteotomy For Mandibular Advancement.

The aim of this investigation was to compare the skeletal stability of three different rigid fixation methods after mandibular advancement. Fifty-five class II malocclusion patients treated with the use of bilateral sagittal split ramus osteotomy and mandibular advancement were selected for this retrospective study. Group 1 (n = 17) had miniplates with monocortical screws, Group 2 (n = 16) had bicortical screws and Group 3 (n = 22) had the osteotomy fixed by means of the hybrid technique. Cephalograms were taken preoperatively, 1 week within the postoperative care period, and 6 months after the orthognathic surgery. Linear and angular changes of the cephalometric landmarks of the chin region were measured at each period, and the changes at each cephalometric landmark were determined for the time gaps. Postoperative changes in the mandibular shape were analyzed to determine the stability of fixation methods. There was minimum difference in the relapse of the mandibular advancement among the three groups. Statistical analysis showed no significant difference in postoperative stability. However, a positive correlation between the amount of advancement and the amount of postoperative relapse was demonstrated by the linear multiple regression test (p < 0.05). It can be concluded that all techniques can be used to obtain stable postoperative results in mandibular advancement after 6 months.

Effects Of High Pressure Homogenization On The Activity, Stability, Kinetics And Three-dimensional Conformation Of A Glucose Oxidase Produced By Aspergillus Niger.

High pressure homogenization (HPH) is a non-thermal method, which has been employed to change the activity and stability of biotechnologically relevant enzymes. This work investigated how HPH affects the structural and functional characteristics of a glucose oxidase (GO) from Aspergillus niger. The enzyme was homogenized at 75 and 150 MPa and the effects were evaluated with respect to the enzyme activity, stability, kinetic parameters and molecular structure. The enzyme showed a pH-dependent response to the HPH treatment, with reduction or maintenance of activity at pH 4.5-6.0 and a remarkable activity increase (30-300%) at pH 6.5 in all tested temperatures (15, 50 and 75°C). The enzyme thermal tolerance was reduced due to HPH treatment and the storage for 24 h at high temperatures (50 and 75°C) also caused a reduction of activity. Interestingly, at lower temperatures (15°C) the activity levels were slightly higher than that observed for native enzyme or at least maintained. These effects of HPH treatment on function and stability of GO were further investigated by spectroscopic methods. Both fluorescence and circular dichroism revealed conformational changes in the molecular structure of the enzyme that might be associated with the distinct functional and stability behavior of GO.

Chitosan Nanoparticles Loaded The Herbicide Paraquat: The Influence Of The Aquatic Humic Substances On The Colloidal Stability And Toxicity.

Polymeric nanoparticles have been developed for several applications, among them as carrier system of pesticides. However, few studies have investigated the fate of these materials in the environment in relation to colloidal stability and toxicity. In nature, humic substances are the main agents responsible for complexation with metals and organic compounds, as well as responsible for the dynamics of these nanoparticles in aquatic and terrestrial environments. In this context, the evaluation of the influence of aquatic humic substances (AHS) on the colloidal stability and toxicity of polymeric nanoparticles of chitosan/tripolyphosphate with or without paraquat was performed. In this study, the nanoparticles were prepared by the ionic gelation method and characterized by size distribution measurements (DLS and NTA), zeta potential, infrared and fluorescence spectroscopy. Allium cepa genotoxicity studies and ecotoxicity assays with the alga Pseudokirchneriella subcapitata were used to investigate the effect of aquatic humic substances (AHS) on the toxicity of this delivery system. No changes were observed in the physical-chemical stability of the nanoparticles due to the presence of AHS using DLS and NTA techniques. However some evidence of interaction between the nanoparticles and AHS was observed by infrared and fluorescence spectroscopies. The ecotoxicity and genotoxicity assays showed that humic substances can decrease the toxic effects of nanoparticles containing paraquat. These results are interesting because they are important for understanding the interaction of these nanostructured carrier systems with species present in aquatic ecosystems such as humic substances, and in this way, opening new perspectives for studies on the dynamics of these carrier systems in the ecosystem.