摘要:

A theoretical explanation is advanced consisting of a five stage process for the formation of polygonal ground which consists of stone borders forming regular hexagons and soil centres. One of these stages, namely the onset of convection in a porous soil between temperatures of 0°C and approximately 4-6°C, is studied analytically. Darcy's law is employed but variable permeability is allowed for and a parabolic density dependence on temperature is assumed. It is found that the theoretical predictions of the aspect ratio agree very well with field studies when a constant upper surface heat flux condition is imposed and an upwardly stratified permeability is chosen. Field study data, which agree very well with the theory, are reported in detail.

ISSN:0309-1929    

DOI:10.1080/03091928908208908

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

The development of initially small perturbations in a weakly supercritical zonal shear flow on a β-plane is studied. Two different scenarios of evolution are possible. If the supercriticality is sufficiently small, the growth of a perturbation is stopped in the viscous critical layer regime; for this case the evolution equation (corrected by the inclusion of a quintic nonlinearity) is derived. At greater supercriticality the nonlinearity cannot stop the growth of the perturbation in a linear (viscous or unsteady) critical layer regime, and the evolution is more complicated. Transition to a nonlinear critical layer regime leads to a reduction in the growth rate and to a slowing (but not a stopping) of the increase in amplitude,A. These are connected to the formation of a plateau (S=constant) of widthL=O(A½) in the profile of absolute vorticity,S. Careful analysis reveals that the growth in amplitude ceases only when the whole instability domain (where the slope of unperturbedS-profile is positive) becomes covered again by the plateau.

ISSN:0309-1929    

DOI:10.1080/03091928908208909

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

It is shown, first, that Ekman dissipation plays a stabilizing role in the development of perturbations in a zonal shear flow, by contracting the instability domain of linear theory and by lowering the saturation level for unstable perturbations. Second, it is shown that dissipation introduces a new scale and, consequently, a new type of critical layer (CL) called “the λ-CL” and provides, in a certain parameter domain, a modification of the nonlinear CL called “the λ-nonlinear CL.” There are consequently five CL regimes. For each regime the corresponding nonlinear evolution equation is obtained and the saturation level is calculated. Using these equations it is shown that a perturbation can develop according to one of six scenarios, each of which is described in detail.

ISSN:0309-1929    

DOI:10.1080/03091928908208910

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor

摘要:

A study is made of the relative stability of disparate horizontal wavelengths of two-dimensional, nonlinear, thermal convection between poorly conducting boundaries. Although the narrower horizontal scales grow most rapidly and tend to dominate the cell pattern initially, an asymptotic theory suggests that the cell-size would eventually evolve to one much broader than the layer depth. This prediction of the asymptotic theory is tested against fully nonlinear spectral and finite-difference models. In some selected numerical experiments, the nonlinear models are consistent with the weakly nonlinear theory only in slightly supercritical conditions. At a Rayleigh number above twice critical, the evolution to broad scales does not occur. The cell-size is locked into the narrower cell-size that first grew and stabilized. The results are applied to mesoscale cellular convection in the atmosphere.

ISSN:0309-1929    

DOI:10.1080/03091928908208911

出版商:Taylor & Francis Group    

年代:1989

数据来源: Taylor