Stability of vertical porous penetrative convection with throughflow

(1988). Unconditional nonlinear stability in penetrative convection: Corrected and extended numerical results. Geophysical & Astrophysical Fluid Dynamics: Vol. 43, No. 3-4, pp. 307-309.

The stability of natural penetrative convection arising due to a uniform internal heat source in a vertical porous layer saturated with an Oldroyd-B fluid is investigated. The vertical walls of the porous layer are impermeable and maintained at different uniform temperatures. The energy stability analysis performed reveals that the system is unconditionally stable even in the presence of internal heating in the case of Newtonian fluids, while for viscoelastic fluids the base flow is found to be unstable. As the energy stability analysis of Gill type is unable to decide the stability of the system, the Galerkin method is used to solve the complex eigenvalue problem. The internal heating introduces asymmetry in the basic flow and amounts to the existence of different set of onset modes. The internal heating and stress relaxation parameter facilitates instability of the system while increasing strain retardation parameter discloses stabilizing effect on the system. Moreover, the critical Darcy–Rayleigh number, wave number and wave speed become invariant as Ns becomes large. The streamlines and isotherms presented herein demonstrate the development of complex dynamics at the critical state.

On the stability of transient penetrative convection driven by internal heating coupled with a thermal boundary condition

Enhancements to Deep Turbulent Entrainment

Flow downward penetration of vertical parallel plates natural convection with an asymmetrically heated wall

The linear stability of penetrative convection is investigated for three different undisturbed temperature profiles, each characterized by a stable layer on the top: case A) a two-layer profile with constant but different lapse rate in each layer, case B) a continuous and smooth mean temperature profile with the depth of the unstable layer fixed, and case C) a temperature profile determined by the conduction equation with the surface temperature undergoing a diurnal variation. The increase of the critical Rayleigh number Rc of the unstable layer with increasing stability number S of the top layer is prominent in case A, less appreciable in case B, and also less noticeable for case C. It appears that the relation between the temperature gradient in the unstable layer and that in the stable layer is more sensitive and meaningful than the relation between Rc and S for a smooth temperature profile, especially for case C in which the depth of the unstable layer is not kept constant. The results obtain...

Introduction.- Thermal Convection with LTNE.- Rotating Convection with LTNE.- Double Diffusive Convection with LTNE.- Vertical Porous Convection with LTNE.- Penetrative Convection.- LTNE and Multi-layers.- Other Convection/Microfluidic Scenarios.- Convection with Slip Boundary Conditions.- Convection in a Porous Layer with Solid Partitions.- Convection with Produting Baffles.- Anisotropic Inertia Effect.- Bidispersive Porous Media.- Resonance in Thermal Convection.- Thermal Convection in Nanofluids.- References.

Summary. Linear and nonlinear stability analyses of penetrative double-diffusive convection in a porous medium are performed. Adopting a standard energy method approach yields a nonlinear threshold which is independent of the salt field. An adaptation of a new operative method by Mulone and Straughan (ZAMM 86: 507‐520, 2006) is used to construct a nonlinear threshold which is dependent on the salt field, greatly reducing the region of potential subcritical instabilities. The employment of this operative technique for problems with spatially dependent coefficients, as presented in this paper, is unexplored in the present literature.

This paper investigates penetrative convection in a layer of porous material saturated with water when there is throughflow present. The density is quadratic in temperature. A linearized instability analysis is derived and compared with a weighted non-linear energy stability analysis. A weighted analysis is necessary to achieve a global non-linear stability threshold. Parameter ranges are found where the linear instability boundary is close to the non-linear stability one.

Continuous dependence on the heat source and non-linear stability in penetrative convection

A nonlinear energy stability analysis is presented for the penetrative convection model of Veronis (1963). The critical Rayleigh number boundary determined here ensures nonlinear stability for arbitrary sized initial amplitudes, unlike the conditional results of Straughan (1985).

Instability of penetrative convection in a vertical porous layer with non-Dirichlet temperature conditions

The paper presents arguments in favor of an explanation of the reduction of the ice-covered area in the Nansen basin of the Arctic Ocean (AO) in winter by the so-called “atlantification “ — the strengthening of the influence of waters of Atlantic origin on the hydrological regime of the Arctic Ocean. We hypothesize that the main agent of “atlantification” in theWesternNansenBasinis winter thermal convection, which delivers heat from the deep to the upper mixed layer, thus melting sea ice and warming the near-surface air. To check up this hypothesis we used ocean reanalysis MERCATOR data for time interval 2007–2017. The quantitative criterion of thermal convection, based on the type of vertical thermohaline structure in the upper ocean layer, was applied to access the change of convection depth between climatic values in 1950–1990 and the present time. The main conclusion of the paper can be summarized as the following. Due to a gradual reduction of sea ice in the 1990s, the vertical stratification of waters in theWesternNansenBasinhas changed. As a result, the potential for penetration of vertical thermal convection into the warm and saline Atlantic layer and the consumption of heat and salt content of this layer for warming and salinification of the overlying waters increased, thus leading to additional loss of sea ice in winter.

The observation and representation in general circulation models (GCMs) of cloud vertical overlap are the objects of active research due to their impacts on the earth’s radiative budget. Previous studies have found that vertically contiguous cloudy layers show a maximum overlap between layers up to several kilometers apart but tend toward a random overlap as separations increase. The decorrelation length scale that characterizes the progressive transition from maximum to random overlap changes from one location and season to another and thus may be influenced by large-scale vertical motion, wind shear, or convection. Observations from the U.S. Department of Energy Atmospheric Radiation Measurement program ground-based radars and lidars in midlatitude and tropical locations in combination with reanalysis meteorological fields are used to evaluate how dynamics and atmospheric state influence cloud overlap. For midlatitude winter months, strong synoptic-scale upward motion maintains conditions closer to maximum overlap at large separations. In the tropics, overlap becomes closer to maximum as convective stability decreases. In midlatitude subsidence and tropical convectively stable situations, where a smooth transition from maximum to random overlap is found on average, large wind shears sometimes favor minimum overlap. Precipitation periods are discarded from the analysis but, when included, maximum overlap occurs more often at large separations. The results suggest that a straightforward modification of the existing GCM mixed maximum–random overlap parameterization approach that accounts for environmental conditions can capture much of the important variability and is more realistic than approaches that are only based on an exponential decay transition from maximum to random overlap.

Linear and nonlinear (energy) stability analysis are performed for a layer of couple-stress fluid with different types of internal heat source profiles. The paper presents the numerical and graphical results for couple-stress fluid when it is influenced by an internal heat source and heated from below. Linear instability is performed by normal mode technique and energy method is used for nonlinear stability analysis. The effects of couple-stress parameter and internal heat source on the stability and instability boundaries are analyzed numerically using Chebyshev pseudospectral method.