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我们得到了对流开始非线性状态下两重叠高粘性流体层对流的数值解。这两层高粘性流体与地球的上下地幔一样厚,由一个固定的水平界面分开。考虑了几个热结构和热边界条件,包括一个等温底部边界、一个设定的热流的底部边界和具有绝热下边界的内热结构。对流开始时,由于每层物质的性质相同,下层比上层更不稳定,长水平波长(与下层的厚度成正比)占优势。对物性差异很大的那些层来说,在对流开始时上层更不稳定,短水平波长(比例于上层的厚度)占优势。当选择的物质的性质使两层同样不稳定时,在长波长具有较小最小值的稳定曲线(瑞雷数Ra-波长关系曲线)出现两个极小值。线性稳定结果具有较弱的非线性对流的特征,除非两层物质都不稳定。当两层具有不同的稳定性时,较稳定的层有一个传导温度场,它的流动是由不稳定层的对流流动的粘滞作用驱使的。当两层具有相同的不稳定性时(即使在对流开始瑞雷值仅两倍于临界值时),两层分别对流。当Ra超过临界值足够大时,下层以长波长对流环对流,甚至在线性稳定理论预测为短波长对流环时也如此。上层总是以短波长对流环开始对流。然而,下层上方的上层对流环的下沉热柱体积随着Ra的增大而增大。于是,水平波长(比如层的尺度)不能用来区分全地幔对流和分层地幔对流。在每层物质的性质相同及Ra相同时,都存在着层间机械耦合(下沉热柱覆在上升热柱之上)。当每层物质的性质很不相同以至在对流开始产生短波长对流环时,在下层两个热柱之上的上层有两个热耦合对流环(下沉热柱在下沉热柱之上和边界处的一个剪切带)。就所有被检验过的情况而论,边界两侧存在一个很大的温度差(总和的50％),暗示着在670km间断面处,两层地幔对流也应该有一个很大的温度变化。但与温度有关的粘性也许会减小这个温度差异。对消减带上重力平面异常和板块地震走时异常的解释应该能说明上、下地幔分层对流系统可能的热耦合机制。
We obtain the numerical solution of the convection of two overlapping highly viscous fluid layers under the condition of convection initial nonlinearity. The two layers of highly viscous fluids are as thick as the Earth’s upper and lower mantle and are separated by a fixed horizontal interface. Several thermal structures and thermal boundary conditions are considered, including an isothermal bottom boundary, a set bottom boundary of the heat flow, and an inner thermal structure with an adiabatic lower boundary. At the beginning of convection, the lower layer is more unstable than the upper layer due to the same properties of each layer, and the longer horizontal wavelength (proportional to the thickness of the lower layer) prevails. For those layers with very different physical properties, the upper layer is more unstable at the beginning of convection, and the short horizontal wavelength (proportional to the thickness of the upper layer) is dominant. When the properties of the chosen material make the two layers equally unstable, two minimums appear for the stable curve (Rayleigh number Ra-wavelength dependence curve) with a small minimum at long wavelengths. Linear stability results have weaker characteristics of nonlinear convection unless both layers are not stable. When two layers have different stability, the more stable layer has a conduction temperature field whose flow is driven by the viscous effect of the convective flow in the unstable layer. When the two layers have the same instability (even when the convection starts at twice the Rayleigh value), the two layers convect separately. When Ra exceeds the critical value large enough, the lower convective loop convects with long wavelength, even when the linear stability theory predicts a short-wavelength convection loop. The upper layer always starts convection with a short wavelength convection loop. However, the volume of the descending column in the upper convection loop above the lower layer increases with increasing Ra. Thus, horizontal wavelengths, such as the dimensions of the layers, can not be used to distinguish between the mantle convection and the stratified mantle convection. When the properties of each layer are the same and Ra are the same, there is an interlayer mechanical coupling (the sinking column overlies the rising hot column). When the properties of each material are so different that convection begins to create a short-wavelength convection loop, there are two thermo-coupled convection loops in the upper layer above the lower two thermal columns (the sinking columns are above and below the sinking columns A shear zone at). For all the cases examined, there was a large temperature difference (50% of the sum) on both sides of the boundary, suggesting that there should also be a large temperature change in the two-layer mantle convection at a cross-section of 670 km. But temperature-related viscosity may reduce this temperature difference. Interpretation of abnormity with anomalous gravitational plane anomalies and plate-travel anomalies should explain the possible thermal coupling mechanism of stratified convective systems in the upper and lower mantle.