Peder A. Tyvand

Anisotropic modelling of thermal convection in multilayered porous media

The principle of large-scale anisotropy due to small-scale layering is applied to thermal convection. The motion takes place in a bounded porous medium heated from below. The medium is periodically layered with respect to permeability and therma,l conductivity. The onset of convection as well as slightly supercritical convect,ion are investigated. Anisotropic modelling proves useful even for small numbers of layers as long as the motion is of ‘large-scale convection’ type (Masuoka et al. 1978). The modelling always fails for motion of ‘local convection ’ type.

Thermal convection in a porous medium composed of alternating thick and thin layers

Abstract This paper is a continuation of a recent work by the present authors [ J. Fluid Mech . 118 , 315–339 (1982)]. The previous paper concentrated on buoyancy-driven convection in a porous medium composed of alternating material layers of equal thicknesses. The present work is a study of the limit case where every alternate layer is very thin and has very small permeability. The onset of convection in such a system and the heat flux at slightly supercritical Rayleigh numbers is studied. As in the earlier work, an investigation of the convergence to homogeneous anisotropy is made. Furthermore, emphasis is placed on applications in insulation techniques and convection in snow layers.

Thermal convection in a rotating porous layer

SummaryIt is found in this note that basic results concerning thermal convection in a rotating porous layer may be obtained from known analysis of thermal convection in an (non-rotating) anisotropic porous medium.RésuméOn peut obtenir des résultats de base sur la convection thermique dans une couche poreuse en rotation à partir de lanalyse connue de la convection thermique dans une couche poreuse anisotrope pas en rotation.

Dispersion effects on thermal convection in porous media

The influence of hydrodynamic dispersion on thermal convection in porous media is studied theoretically. The fluid-saturated porous layer is homogeneous, isotropic and bounded by two infinite horizontal planes kept at constant temperatures. The supercritical, steady two-dimensional motion, the heat transport and the stability of the motion are investigated. The dispersion effects depend strongly on the Rayleigh number and on the ratio of grain diameter to layer depth. The present results provide new and closer approximations to experimental data of the heat transport.

Thermal convection in a porous medium with horizontal cracks

Abstract This paper is the second part of a study of thermally-driven convection in a porous medium composed of very thin layers alternating with thick layers of a different material. While in the first part [Int. J. Heat Mass Transfer26, 761–780 (1983)] the thin layers had very small permeability (sheets), here the effects of thin, highly permeable horizontal layers (cracks) are investigated. Even and odd numbers of layers are studied separately, with a variety of results being given for the critical Rayleigh number and the subsequent heat transport for slightly supercritical convection. Calculated streamline patterns indicate that local, or smallscale, convection is generally absent for the present problem. In the earlier paper, it was shown that a sheet tended to ‘close’ a constant-pressure upper surface—it is found here that, conversely, a crack in contact with an impermeable boundary tends to ‘open’ that surface. Odd numbers of layers give either zero or two cracks in contact with the boundaries—in the latter case there is good convergence towards homogeneous anisotropy as the number of layers increases. The results have application to, for example, insulation problems where gaps can occur between successively applied layers of insulating materials.

Heat dispersion effect on thermal convection in anisotropic porous media

Abstract The effect of hydrodynamic dispersion on the onset of thermal convection in flows through anisotropic porous media is studied theoretically. The porous layer is homogeneous and bounded by two infinite perfectly-heat-conducting impermeable horizontal planes kept at constant temperatures. Horizontal isotropy with respect to permeability and thermal diffusivity is assumed. A pressure-driven basic flow is considered in the limits of small and large Peclet numbers. The analysis shows that the onset of convection in both cases is independent of longitudinal dispersion, while dispersion in lateral directions has stabilizing effects. The preferred mode of disturbance consists of stationary rolls with axes aligned in the direction of the basic flow.

Thermal convection in a porous medium with continuous periodic stratification

Abstract The onset of convection in a horizontal stratified porous layer heated from below is studied theoretically. The stratification is continuous and periodic, with N/2 periods within the layer. For large numbers of N the critical Rayleigh number converges towards the limit of homogeneous anisotropy with a deviation proportional to N−2.

Decay of a disturbed free surface in a layered porous medium

Abstract The gravitational decay of a free surface of fluid within a porous medium is studied theoretically. The porous medium consists of two superposed horizontal layers of different permeabilities, resting on an impermeable bottom. A formula for the decay rate is found, valid for small amplitudes of disturbance.

Transient free-surface groundwater flow due to an array of circular drainage ditches

The present paper is a numerical study of a transient free-surface flow into an array of circular drainage ditches in a porous medium. By the boundary integral equation method and a semi-Lagrangian description of motion, the groundwater table is tracked as a function of time. Primarily, we consider the case of atmospheric pressure along the ditch contour. An analytical small-time expansion is presented in an appendix. In contrast to the case of constant flux into a sink (Papatzacos, 1989), there is no cusp formation at the free surface. The flux into a ditch is approximately a linearly decreasing function of time. We also include a second version of the boundary condition at the ditch; parts of its contour are impermeable.

A note on gravity waves in a viscous liquid with surface tension

SummaryThe linear theory by Reid [1] on gravity waves in a viscous liquid with surface tension is extended. Asymptotic formulae for the dispersion relation are derived. A critical Morton number equal to 0.044789 is found. Only in liquids with smaller Morton numbers, travelling ripples may exist with group velocity exceeding phase velocity.ZusammenfassungReids lineare Theorie über Gravitationswellen in einer viskosen Flüssigkeit mit Oberflächenspannung wird erweitert. Abgeleitet werden asymptotische Formeln für das Verteilungsverhältnis und eine kritische Morton-Zahl gleich 0.044789 wird gefunden. Nur in Flüssigkeiten mit geringeren Morton-Zahlen existieren wandernde kleine Wellen mit einer Gruppengeschwindigkeit, die die Phasengeschwindigkeit überschreitet.