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In the present paper, double-diffusive convection, taking into account Coriolis effects, in a horizontal layer of Brinkman-anisotropic bi-disperse porous medium is analysed. Via linear instability analysis, we find that convection can set in through stationary or oscillatory motions and the critical Rayleigh numbers for the onset of stationary secondary flow (steady convection) and overstability (oscillatory convection) are determined. [ABSTRACT FROM AUTHOR]

An investigation of the basic nanoconvective flow to be applied in evaluating the limit of validity of the transient hot wire experimental (THW) method for nanofluids is presented. Analytical solutions for the basic temperature, basic nanoparticles volume fraction, and basic natural convection velocity are being derived and analyzed. These basic solutions are needed in follow-up linear and nonlinear stability analyses aiming to establish the time required for natural convective heat flux to develop and invalidate transient hot wire experimental results. While the first part of the paper presents the current status of knowledge related to the transient hot wire experimental method and the theoretical aspects governing the validity of the method, the second part aims at presenting new results that can provide additional and more accurate conditions for the validity of that experimental method. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate the effect of a vertical constant throughflow on convective instabilities in a horizontal layer of fluid-saturated bi-disperse porous medium heated from below. Via linear instability and nonlinear stability analyses of the throughflow solution, the linear and nonlinear critical Rayleigh numbers for convective instabilities have been determined and studied as functions of the strength of the throughflow. [ABSTRACT FROM AUTHOR]

In the present paper, the effect of the Vadasz inertia term on the onset of convective motions for a Darcy–Brinkman model is investigated. It is proved that this term leads to the possibility for oscillatory convection to occur. Hence, convection can occur via either oscillatory or steady motions. It is proved analytically that the onset of steady convection is not affected by the Vadasz term, while oscillatory convection is favoured by it. Moreover, conditions to rule out the occurrence of oscillatory convection are determined numerically. The influence of rotation, interaction coefficient and mechanical and thermal anisotropies on the onset of instability is investigated, both analytically and numerically. [ABSTRACT FROM AUTHOR]

Perfectly incompressible materials do not exist in nature but are a useful approximation of several media which can be deformed in non-isothermal processes but undergo very small volume variations. In this paper, the linear analysis of the Darcy-Bénard problem is performed in the class of extended-quasi-thermal-incompressible fluids, introducing a factor β which describes the compressibility of the fluid and plays an essential role in the instability results. In particular, in the Oberbeck-Boussinesq approximation, a more realistic constitutive equation for the fluid density is employed in order to obtain more thermodynamically consistent instability results. The critical Rayleigh-Darcy number for the onset of convection is determined, via linear instability analysis of the conduction solution, as a function of a dimensionless parameter β ^ proportional to the compressibility factor β , proving that β ^ enhances the onset of convective motions. Article Highlights: The onset of convection in fluid-saturated porous media is analyzed, taking into account fluid compressibility effect. The critical Rayleigh-Darcy number is determined in a closed algebraic form via linear instability analysis. The critical Rayleigh-Darcy number is shown to be a decreasing function of the dimensionless compressibility factor. [ABSTRACT FROM AUTHOR]

Thermal convection in a fluid saturating an anisotropic porous medium in local thermal nonequilibrium (LTNE) is investigated, with specific attention to the effect of variable viscosity on the onset of convection. Many fluids show a remarkable dependence of viscosity on temperature that cannot be neglected. For this reason, we take into account a fluid whose viscosity decreases exponentially with depth, according to Straughan (Acta Mech. 61:59–72, 1986), Torrance and Turcotte (J. Fluid Mech. 47(1):113–125, 1971). The novelty of this paper is to highlight how variable viscosity coupled with the LTNE assumption affects the onset of convection. A numerical procedure shows the destabilising effect of depth-dependent viscosity. Moreover, it comes out that the LTNE hypothesis makes the influence of viscosity more intense. Linear instability analysis of the conduction solution is carried out by means of the Chebyshev-tau method coupled to the QZ algorithm, which provides the critical Rayleigh number for the onset of convection in a straightforward way. The energy method is employed in order to study the nonlinear stability. The optimal result of coincidence between the linear instability threshold and the global nonlinear stability threshold is obtained. The influence of anisotropic permeability and conductivity, weighted conductivity ratio, and interaction coefficient on the onset of convection is highlighted. [ABSTRACT FROM AUTHOR]

It is well known that when a horizontal layer of fluid is heated from below, a thermal boundary layer of less dense and hot fluid rises up. When this boundary layer becomes unstable, convective motion in the fluid above sets in. Forecasting when instabilities take place is essential. When a salt dissolved in a fluid saturating a porous medium heated from below is considered, simultaneous mass diffusion and thermal diffusion occur. Unlike the diffusion of heat, the diffusion of salt can take place only through the fluid phase, so an additional physical effect has to be considered: the Soret effect, that is the mass flux created by a temperature gradient. In the present paper the onset of convection in a rotating layer of bi-disperse porous medium saturated by a binary fluid mixture, taking into account the Soret effect, is analysed. Linear stability analysis is performed in order to determine the instability thresholds for the onset of convection via a steady state (stationary convection) and via an oscillatory state (oscillatory convection). Nonlinear stability analysis is performed to obtain the global stability threshold with respect to the L 2 -norm. [ABSTRACT FROM AUTHOR]

The onset of natural convection in a fluid-saturated anisotropic porous layer, which rotates about the vertical axis, under the hypothesis of local thermal non-equilibrium, is analysed. Since the porosity of the medium is assumed to be high, the more suitable Darcy-Brinkman model is adopted. Linear instability analysis of the conduction solution is carried out. Nonlinear stability with respect to L 2 -norm is performed in order to prove the coincidence between the linear instability and the global nonlinear stability thresholds. The effect of both rotation and thermal and mechanical anisotropies on the critical Rayleigh number for the onset of instability is discussed. [ABSTRACT FROM AUTHOR]

Thermal convection in a horizontally isotropic bi-disperse porous medium (BDPM) uniformly heated from below is analysed. The combined effects of uniform vertical rotation and Brinkman law on the stability of the steady state of the momentum equations in a BDPM are investigated. Linear and nonlinear stability analysis of the conduction solution is performed, and the coincidence between linear instability and nonlinear stability thresholds in the L 2 -norm is obtained. [ABSTRACT FROM AUTHOR]

The onset of thermal convection in an anisotropic horizontal porous layer heated from below and rotating about vertical axis, under local thermal non-equilibrium hypothesis is studied. Linear and nonlinear stability analysis of the conduction solution is performed. Coincidence between the linear instability and the global nonlinear stability thresholds with respect to the L2—norm is proved. Article Highlights: A necessary and sufficient condition for the onset of convection in a rotating anisotropic porous layer has been obtained. It has been proved that convection can occur only through a steady motion. A detailed proof is reported thoroughly. Numerical analysis shows that permeability promotes convection, while thermal conductivities and rotation stabilize conduction. [ABSTRACT FROM AUTHOR]

The onset of thermal convection in an electrically conducting fluid saturating a porous medium, uniformly heated from below, salted by one chemical and embedded in an external transverse magnetic field is analyzed. The critical Rayleigh thermal numbers at which steady and Hopf convection can occur, are determined. Sufficient conditions guaranteeing the effective onset of convection via steady or oscillatory state are provided. [ABSTRACT FROM AUTHOR]

The onset of porous convection in an electrically conducting fluid uniformly heated from below and embedded in an external transverse constant magnetic field is analysed. In particular the effect of Vadasz inertia term, measured through the Vadasz number $$V_a$$ , on the instability threshold, is investigated. For the three-dimensional perturbations and full nonlinear problem it is shown that sub-critical instabilities do not exist and the global nonlinear stability is guaranteed by the linear stability. The long-time behaviour is characterized via the existence of $$L^2$$ -absorbing sets. [ABSTRACT FROM AUTHOR]

A reaction-diffusion system modeling cholera epidemic in a non-homogeneously mixed population is introduced. The interaction between population and toxigenic Vibrio cholerae concentration in contaminated water has been taken into account. The existence of biologically meaningful equilibria is investigated together with their linear and nonlinear stability. Using the data collected during the Haiti cholera epidemic, a numerical simulation is performed. [ABSTRACT FROM AUTHOR]

A system modeling fluid motions in horizontal porous layers, uniformly heated and salted from below, is analyzed in the case of variable thermal and solutal diffusivities. The boundedness and uniqueness of solutions are shown. A class of non-constant throughflows is found and their stability is analyzed via a new approach. Conditions of global nonlinear stability, in closed form, are obtained. [ABSTRACT FROM AUTHOR]

A reaction-diffusion system modeling the predation between two species is analyzed in the case in which the predators have to search, share and compete for food. The boundedness and uniqueness of the solutions is proved and conditions guaranteeing the global nonlinear asymptotic stability of the positive equilibrium point have been found. These conditions improve those ones present in the existing literature. [ABSTRACT FROM AUTHOR]

The linear and nonlinear stability analysis of the motionless state (conduction solution) and of a vertical throughflow in an anisotropic porous medium is performed. In particular, the effect of a nonhomogeneous porosity and a constant anisotropic thermal diffusivity have been taken into account. [ABSTRACT FROM AUTHOR]

Linear and nonlinear stability analyses of vertical throughflow in a fluid layer, where the density is quadratic in temperature, are studied. To avoid the loss of key terms a weighted functional is used in the energy analysis. Both conditional and unconditional thresholds are derived. When the throughflow is ascending the linear and nonlinear boundaries show substantial agreement. The linear boundary remains close to the conditional nonlinear boundary for descending throughflow, whilst the unconditional threshold begins to diverge. [ABSTRACT FROM AUTHOR]

The paper concerns the Beddington–De Angelis predator-prey model, under Robin boundary conditions. General properties—such as boundedness, uniqueness and existence of invariant regions—are obtained. Linear stability (instability) threshold of the equilibrium state S (biologically meaningful) and diffusion-driven instability (Turing effect) are studied. In the framework of nonlinear L 2-energy stability, conditions guaranteeing stability and local attractiveness are obtained. [ABSTRACT FROM AUTHOR]

A correction to the article "Influence of diffusion on the stability of equilibria in a reaction-diffusion system modeling cholera dynamic," that was published in a previous issue of the journal is presented.